Class 11 Physics Complete Formulas for NEET 2026 Part - 2 | Subrat Sir | #NEETPhysics

Añadido: 2026-05-04

[00:00:02]Hello.

[00:00:15]>> Okay. Okay. Okay. Hi everyone. Welcome back. Welcome, welcome back my dear friends. Hello.

[00:00:23]Good afternoon.

[00:00:27]Welcome back to PW Neat English.

[00:00:31]How are you all? Today we'll continue physics formula one short of class 11 part two. If you have missed part one, we have already completed part one till I believe gravitation or rotation right and from there we are going to continue and complete part two in today's class.

[00:00:53]Along with this, let me tell you for class 12th, we are going to complete formulas of class 12th in our next life class in one go. Right? So, uh you're going to get all the formulas of class 11th and 12th of physics by next life class. Right? Okay. Hi everyone. I am all good. How are you all? Quickly write down in the chat box. And as you guys know from the last live class, it is not only about formulas. We are completing all the graphs. We are completing all shortcut formulas. We are also talking about some of the very important notes.

[00:01:33]Uh for example, in motion under gravity, we have done we have also included notes like ratio of displace ratio of distance traveled in in first, second, second, second, third, second. Right? So I'm just giving you one example just like this. We are going to complete important notes along with formulas all formulas for all chapters. Right? So if you want to have a quick revision for physics this is going to be the best thing to do right along with this obviously you have to solve pyqs of need you have to solve some of the pyqs of mains. As we know that nta can directly give pyqs from mains into need. They have done it last time in N 2025. They can do it again in N 2026. Right now without any delay, let's start. Everyone's ready. Shall we begin?

[00:02:26]My dear friends, shall we begin quickly? Let me check. Hopefully everything is clear, right?

[00:02:38]Okay, fine. Let's go then.

[00:02:46]done. So my dear friends, the first topic that we are going to start today, the first lecture uh first chapter that we are going to talk about today is mechanical properties of solids. Right?

[00:03:00]It's a very small chapter. So complete all the formulas that's given in this particular chapter. For example, is we going to start with stress and in stress we are going to first talk about longitudinal stress that is normal stress. Right? Formula is simple force upon area.

[00:03:16]Force upon area. Please remember the unit. Please remember that this is the restoring force divided by area. This is the external force that we are applying because of which there will be deformationation in the rod and we are going to talk about that as well. Right?

[00:03:31]So this is very basic formula but do remember it. Remember it's unit stress and then we are going to also talk about volutric stress right when basically we are going to also discuss this thing in fluid mechanics in chapter of fluid mechanics. If you remember that we usually get a quotion like that we have got a sphere and when we drop it down up to a depth of h right its radius changes. So we can calculate volutric stress also and we can als uh this is basically pressure we can write it down as ro g and we can also talk about strain right. So this is again force upon area and this thing can be written as pressure right this thing can be written as pressure. This is that stress which is responsible to change the volume of the body. And then you have got shearing stress. Let me tell you one thing. Let me tell you one thing that if you want me to compare uh the importance of all of these formula then everyone knows from PYQs that this is most important then comes this and usually they don't give quotients from shearing stress but that doesn't mean that they are going to do the same thing in need 2026 all right so please do not completely rely on need on uh need PYQ's data NTA can also surprise you let's suppose that NTA has not given any question for past five years or h or it has given minimum questions from a particular topic then they can also surprise you to think like this also right think like this also please try to understand what I'm trying to say do not completely rely on on pyq's next thing is going to be so these are pretty simple formula next thing is about longitudinal strain volutric strain and shearing strain so basically strain is simp simple thing that is change in length upon original length, right? Change in length upon original length. Now, please understand this thing that what they can do is along with formulas, it's not only about me reading these these formula in this class. I'm also letting you know from where usually NTA frames questions.

[00:05:42]So usually what happens is that they talk about longitudinal strain, they talk about longitudinal stress, they talk about Young's modulus and they relate this with thermal properties of matter. Are you getting it what I'm trying to say? So because of thermal because of heat there will be linear expansion and then we can also talk about uh we can also talk about longitudinal stress also. Right? So this is very very important. I think in N 2025 they have done this or NE 2024 I believe right. Similarly so similarly I have already told you that they are going to frame a question a combined question from fluid mechanics and volutric stress right. So remember this strategy till now I have not seen many problems from shearing stress but do not skip this as well. And then you have got long volutric stress again change in volume divided by original volume. And then you have got shearing strain whose formula is slightly different. Please remember for shearing stress what we do is that this end remains fixed. This end remains fixed and we apply a force which is tangent tangent to this side. And then this is small angle theta and let's say this is x. So this is volutric strain that is theta divided by theta / x or sorry we can rewrite this as delta x divided by l right. So delta x divided by l and that will be written as theta or 5 whatever you want to call it. So this is shearing stress. Now comes my dear friends very very important thing and see I have written each and everything over here. It's not only about formulas or not only about graphs.

[00:07:29]We have got graphs. Any modulus of elasticity can be written as stress divided by strain. Again, most probably uh if you are going to analyze the pyq data, mostly they have talked about Young's modulus, right? So, but still general formula is stress upon strain.

[00:07:48]This is Hook's law, right? When stress is directly proportional to strain, that means material is obeying Hook's law.

[00:07:55]Now the next thing is you can also remember that tan theta is actually equals to modulus of elasticity. If we are talking about graph between stress and strain quickly write down in the chat box everything's going good right this is the best way to revise chapters very quickly. Next thing is for a for a rigid body. What do you mean by a rigid body? My dear friends, if they are talking about a rigid body, it means that let's suppose this is a rigid body, right? What is the definition of a rigid body? It means that let's take any two points. Let's take point A. Let's take point B. We are going to say that the separation between these two points will never change. We can we can define it using velocities also. But it let's let's simply say that separation distance between any two points will not change that makes a body rigid body. Right? So if we have got a rigid body that means it's not going to deform. So that means it's its modulus of elasticity is going to be infinity.

[00:08:58]All right clear? Is there any doubt? Let me know in the chat box.

[00:09:03]And please remember some of the very basic things. These things are from NCERTT also. Uh steel is more rigid than uh rubber, right? And the modulus of uh elasticity depends upon the nature of the metal. It depends upon the temperature, right? And then you have got and it is independent of dimensions.

[00:09:22]This is also very important that it is independent of dimensions. Then you have got modulus divided by bulk modulus.

[00:09:29]Sorry, Young's modulus can we can talk about three types of modulus of elasticity over here. First is Young's modulus. Then we have got bulk modulus and then we have got modulus of rigidity. So please remember this thing.

[00:09:42]Hopefully everything is clear. Quickly write down in the chart box. We have done we have completed the graph. We have completed Hook's law and we have also talked about types of modulus of elasticity. Then comes this graph that is stress strain curve because they have not asked anything from stress strain curve for I think for a couple of years.

[00:10:05]Then you can also think like this that okay they have not asked this particular problem from this chapter and always NTA gives one question from this chapter. So you can actually you can make your own strategy that this time they might ask something from here right. So always remember that along with PyQ from PYQ we are going to only analyze and we'll get to know what type of questions they ask but that doesn't mean that every time they are going to ask a question from a particular topic unless and until we are talking about modern physics from modern physics there are three or four uh important topics from a particular chapter from dual nature there are three important topics from atoms there are three important topics there is 90% certaintity that they are going to ask question from there Right? But that is not the case when we are going to talk about class 11's physics because we have got lots of topics over here. So in stress strain curve please remember as far as stress is directly proportional to strain that means body is following Hook's law. That means body has the ability to regain its original shape and size. This is called as elasticity.

[00:11:14]Please remember the ability of a body to regain its original shape and size.

[00:11:18]Since steel is more elastic than rubber for this specific case that you are going to apply force on a steel deformation deformation will take place and then there will be a restoring force that will act on the steel which will make which will which will make that steel to reform its original shape and size. Right? That's not the case for rubber. And the reason is that after this point what's going to happen is that the relationship between stress and strain is going to be not directly proportional. And then I have written each and every uh each and every point statement for you. Right? You also know that this is from NCERTT very very important. Please remember it. That means A is proportional limit. That means till A stress is directly proportional to strain. Then AB stress is not proportional to strain but body regain its original shape and size. Got it? So between A and B there the proportion it's not directly proportional but still body retains its elastic property right it if we are going to remove the deforming force body will regain its original shape and size right after B is called as yield point that means after B body does not regain its original shape and size so please remember yield after yield point body is not going to come back to its original shape and size and beyond B we are going to call that it is a plastic What is opposite of elastic? It is plastic.

[00:12:43]Plastic does not regain its original shape and size. Quickly write down in the chat box if everything's going good till here. Be quick. Right. Solid. After this you have got ultimate stress point that is called as D. Kindly look at the graph also because beyond D even if you are going to be D if you're going to apply a very small force then strain is going to be relatively large right. So large strain is produced even for a small applied force and E is called as the fracture point. Got it? Clear right.

[00:13:17]Please kindly see how important all of these things is within minutes we are completing entire topics along with graphs. So although uh I have told you that we are going to only talk about formulas. Now if we are only talking about formulas we can we can complete that this is formula. Now let's move to the another formula. But we are not doing that. We are also completing all sorts of graphs, all sorts of important points. Right? So note this that this is going to be really beneficial for you if you want to revise in last few days. Next thing is my dear friends, let's compare two materials. If they'll give you two graphs, how are you going to compare it?

[00:13:55]Right. Right. So let's suppose you have got two materials. One is a material and second is this material. How are you going to find out which material is most more elastic or I can also call which material is more ductile. Have you ever heard about ductility right? If we if we can actually draw uh bodies into like for example as gold is highly ductile and malleable right so that ductility property if let's suppose we are talking about these two region so plastic region is large for ductile materials and smaller for britter materials that means you can stretch it the plastic region is is very very large please remember plastic region is that region that after removing the deform forming force the body is not going to come to its original shape and size. Got it? So plastic region should be large. If plastic region is small what does it mean? It means that fracture point will will come soon. And if fracture point comes soon comes soon that makes body brittle. Brittle means like for example as glass is brittle. If you're going to drop a glass it will it will shatters into pieces right? So brittle basically means that fracture point is nearer to the plastic region. So plastic region is small that makes a particular material as a brittle material. If plastic region is large that makes a material as ductile material. So this material a material is more suitable to draw to to to stretch. Got it sir. last class K notes I'm trying my best to get you notes from last class right hopefully when we are going to I'll do one thing when we are going to complete all of these lecture I will definitely compile I I'll ask the team to compile all the notes into one single PDF and I'll get it to you right got it I will I will get PDF wait for some more time you will get the PDF all Right. Next is my dear friends Young's modulus. All right. So for Young's modulus now this is actually very important according to PyQs. So do not miss it.

[00:16:06]Do not miss this my dear friends. So Youngs modulus is Young's modulus is basically my dear friends if you if you want me to write down the formula.

[00:16:15]Young's modulus is basically longitudinal stress divided by longitudinal strain.

[00:16:28]That means force upon area time change in length upon original length. Now they are not going to give you a simple problem a direct problem from Young's modulus. They are going to definitely try to include one thing or the other.

[00:16:42]So be prepared that if you're going to get a problem from Youngs modulus they will they will use a crossover question to test this right but this is all simple like for example as the first crossover question can be let's suppose we are comparing it with a spring constant K that means first write down the force using this formula so when you are going to write down force using this formula my dear friends force can be written as Y into A into delta L uh Y into A into delta L divided by original length L. Got it? So please remember that force can be written like this and you can also memorize it. And after that force can be also written as kx. Got it? Over here instead of delta L I can write delta X. Instead of change in length I can write either elongation or I can write compression for a for a for a spring. Quickly write down in the chat box if things clear till here.

[00:17:38]Right? For a spring I can write instead of delta L I can write down X. Now over here you can write down force equals to this and equals to kx. So kx over here is spring force. kx over here is a spring force.

[00:17:57]Hopefully everything is clear. Comparing these two you can you can finally get the formula of spring constant in terms of Young's modulus. This is very important. Please, please understand that using Young's modulus how to find out spring constant and after knowing it you can remember it. Now moving on to the next thing.

[00:18:20]The next important thing is right now we are talking about Young's modulus. Next important thing is if you are stretching a particular body then you are doing some work to stretch it. We can calculate that work done. How we can calculate that work? because we know how much force is required and let's suppose x is the displacement. So force multiplied by x is going to be work done. Obviously force is variable. So we need to integrate it. But finally after doing all of these things or we can directly write/ kx² you know that we we have derived this half kx formula in potential energy stored in a spring also. So similar force similar potential energy will be stored over here as well.

[00:19:00]Right. So/ kx² and we we have calculated the value of kx. So you can rewrite this formula in various terms. Kindly see that this is this was the value of k y a divided by l. So 1 upon 2 y a / l into x². Most important thing is these two formulas.

[00:19:22]So my dear friends y can be written as stress divided by strain. Clear? A * X can be written as volume and one more X square can be written as strain. Right?

[00:19:33]So please remember this thing how we have written this formula. Let me tell you 1 upon 2 instead of Y we have written stress upon strain.

[00:19:43]Stress upon strain and please remember in this all of these cases we are writing strain as change in length divided by original length. So let's say original length is L. Right? Let's say original length is L. Clear? So Y can be written something like this. Then you have got A, you have got X and then you have got X². So can I write instead of X² can I write sorry instead of X can I write strain squared * L². Correct? So just substitute the value of X² over here and you will get these two formulas. So 1 upon 2 stress by strain time volume into strain square or you can write 1 upon2 stress time strain into volume. One more important thing yes that is energy density that they have written over here that is if you are going to divide elastic potential energy with volume you're going to get elastic energy density or energy density that will be one upon two stress time strain. Please remember one upon two stress strain strain is not potential energy not work done but it is potential energy divided by volume and remember volume over here volume we have written as obviously a * l a * l let me know in the chat box if every formula is clear from here be quick done can we move on sorted All right, moving on to the next one.

[00:21:31]Then you have got see I have included all the important notes also. These these two things basically comes as questions.

[00:21:41]First one is first one is my dear friends increase in length due to its own weight.

[00:21:49]Increase in length due to its own weight.

[00:21:54]And you can directly remember the formula the this comes out to be 1x4 this formula comes out to be 1x4 * n² g² l / g a how we are going to do it I'll explain it to you my dear friends what you can actually assume over here is that we have got our we have got a rope and the entire mass is actually suspended at this point so the original length actually instead of L it becomes LX2 and then you can apply your normal formula that F can be written as Kx and instead of F we have got MG and my dear friends then instead of K we can rewrite the formula that we have derived over here that we have derived over here right we have already derived this K formula so directly substitute it over here and then you can find out the value of you can find out the value of potential energy and you can to find out the value of x. So please remember these are two very important formulas. It is going to save a lot of time if they are going to tell you that we have suspended a 2 kg block, we have suspended a 10 kg block or we have suspended a m kg block.

[00:23:08]So this is going to be extension remember and this is going to be potential energy. I'll write it down over here. This is going to be potential energy. All right, everything's clear.

[00:23:24]Let me know in the chat box. Done. The next thing is my dear friends, similarly let's suppose we have got two blocks.

[00:23:33]This was a rod. That's why we are calling increase in length due to its own weight. So this rod has got mass, right? It is not a massless rod. Whereas these strings have these strings are massless. So this is these strings are massless and then we have connected blocks u with this with this uh string and we have connected mass m and 2m. So simply apply the formula of X that is MGL divided by 2 Y A instead of this two please remember I have written this two we have written this two because of this L by2 and this LX2 came because we have assumed that instead of this one complete rod let's assume we have got a massless string and then the entire mass of this rod which is M is suspended at its midpoint.

[00:24:28]So the length of the string becomes Lx2.

[00:24:31]But here the length of the string is let's suppose normal L1. So we are going to write 3 mg L1 divided by Y1 into A1.

[00:24:38]Got it my dear friends? Quickly write down this thing in the chart box if everything's clear. And similarly for X2 we are going to write f_sub_2 divided by k2. And then we are going to substitute the value of f_sub_2 and k2. So the ratio will come out to be this. Please remember all of these things are slightly above your need level but they can ask something from here. There is chances are less. It's not like extremely important but they can ask.

[00:25:05]But please remember this. This is important. And remember the value of X also do not apply direct formula of X for a string because this is for a mass rod. This is for a rod which has got some mass. All right. Hopefully you are understanding all of these things. So this is for your result. And then last one is please understand that I am also giving you less notes from bulk modulus because from mechanical properties of solid uh which is highly important.

[00:25:36]Young's modulus is highly important.

[00:25:38]Then we are going to also talk about bulk modulus in fluid. Why? Because again I have explained it to you that they're going to give a quotion from bulk modulus combined with fluids.

[00:25:48]Right? So bulk modulus says we have we already know this B can be written as minus delta P divided by delta V by V and you know why we write this minus sign that is very important because when you are going to increase pressure volume is going to decrease for that we have got a negative sign because we want beta we want bulk modulus to be to be a positive value right now we have got two things over here please remember that bulk modulus for an isoothermal process is equals to P. Bulk modulus for an adiabatic process is equals to gamma * P and bulk modulus from for any isotropic process will be X * P. Right? And then you have got last is you have got modulus of rigidity. These two formulas are sufficient for in mechanical properties of solids. For practicing of quotient practice crossover topics from both of these things.

[00:26:45]All right my dear friends. Now let's move to fluid. Everything's clear. First chapter over right done. You are going to get this PDF. Wait for some more time. I've got one more lecture left for formula revision. In that I'm going to complete class 12th in one go. And then you can have you can have your PDF right. I'll compile all of these in one file and then I I'll I'll get it to you in description box or through any means.

[00:27:13]But I'll get it to you. Next is my dear friends pressure right? So this is very basic you don't have any doubt in in the formula for pressure right this is also again very basic thing that pressure is equals to ro gh that at any depth the pressure applied will be ro gh this is the pressure this is the axis pressure obviously if let's suppose this is the surface if let's suppose this is the surface and we are talking about a point over here then this and let's say this height is h and this point is a Then pressure at point A will be actually atmospheric pressure plus ro gh obviously right. So ro gh is the axis pressure. Now my dear friends please remember the hydrostatic paradox very simple thing that pressure at point A B C and D all will be same right and god pressure is basically means pressure at any point absolute pressure at at any point minus atmospheric pressure. Got it? minus atmospheric pressure and atmospheric pressure is written as 1.01 into 10 ^ 5 pascal. If let's suppose you want to save some time, you can also remember atmospheric pressure as sometimes you can rewrite this thing as 1 into 10 ^ 5 pascal.

[00:28:32]Got it? For have for having quick calculations, you can also use this.

[00:28:38]Now my dear friends, this is a YouTube manometer. Although again NTA has not asked direct questions from here but they can do this year right again I'm saying that watch the pattern of last year and then try to add something new also into your preparation. Now we are going to solve this question. We have got a relation over here but I'll explain how to solve it. See you need to re you need to write down the pressure from any one side right. So let's write down pressure from this side. Over here we have got it is exposed to atmospheric pressure. Now let's come down to this point. So this height is H1. So pressure of this point my dear friend will be pressure of point A will be atmospheric pressure plus row G into H1. Now the point is my dear friend this is a same liquid. So same liquid at same level will have same pressure. So that means pressure at point B can be written as again atmospheric pressure plus this is the axis pressure that means row G into H2 and because point B and point A happens to be in the same liquid and at the same level that means that P A and PB will be same that means P not and P not will get cancelled out G and Ro G will get cancel out right I'm so sorry I'm so sorry G and G will get canceled out and as far as densities is concerned. This is density row 1. This is density row 2. So we'll have h1 into d1 and h2 into d2. I have used row. Usually we use row. In this diagram they have used a d. Is everything fine? Clear? So please understand how we write down equation for a manometer. It is very very simple thing right? They are going to ask you to find out density or find out height and they are going to give you the other two values other three values sorry.

[00:30:30]Similarly, can you understand when they are going to give an equation something like this, what the point is that this point is common. This point is common.

[00:30:40]The the interface, the boundary, understand the boundary. Everything clear? All right. Quickly write down in the chat box if all of these diagrams are clear. See again these diagrams do not come under formulas. Why I'm telling you? because I'm I'm trying to give you a an honest revision. This is not just about me giving you formula reading formulas. Understand these things also along with the formulas. Okay? Please remember that this is density is D1. So let's write down the pressure of this point from from here from here. Right?

[00:31:14]So atmospheric pressure let's say this is point A. So we are going to first write down the pressure from this side.

[00:31:20]So atmospheric pressure P plus my dear friends this height is H1. So we are going to write density this time I'll also use density d1 row g into h1 and then we are going to do the same thing from here. So P plus row instead of row let's write D2 into G into H2.

[00:31:42]Same logic my dear friends and you're going to get the same result also.

[00:31:47]Right? Now let's suppose if one of them is water, if one of the liquid is water then you can write down the relative density also. Right? So density of any liquid divided by density of water gives me relative density. So you can you can all this is nothing some this is not something new always remember the uh formula for relative density and specific gravity right means the same thing now let's move on and please understand this also that is mixing of liquid be quick quickly write down in the chat box if everything's clear till here if everything's clear with these two diagrams of YouTube manometer right everything's good Robin soashri Let's keep the chat for asking doubt and quickly let me know if everything's clear. Then I'm going to move to mixing of liquid. Be quick.

[00:32:43]Be really really quick. Got it?

[00:32:48]Done. Now comes mixing of liquid. In mixing of liquid they can ask about the resultant or final density. Now final density will be the sum of the arithmetic mean of the two densities. If volumes of the liquids are equal, this is the most important thing. If volumes of the liquid are equal, then directly use this formula. Do not waste any more time. All right, be quick. My dear friends, let's keep the chat for asking doubts. Give some attention to these things. Most of the students are going to skip many of these formulas because they will not have any time. All of your time will be spent uh in revising important topics like modern physics, electromagnetism, chyatics, units and dimension and you are going to most of the time students skip four chapters.

[00:33:41]Let me name those four chapters.

[00:33:43]Mechanical properties of solids, mechanical properties of fluids, thermal property. In thermal property we have got heat transfer. You don't re actually realize because in need we we only name the chapters according to NCERTT mechanical properties of fluids is not one single chapter. We have got lots of thing in that right. So do do not miss uh these chapters. You're going to get one one one question from each of these sub chapters. One chapter from hydrostatic fluid, one chapter from fluid mechanics, one chapter from surface tension. All of these chapters are all of these subtopics are chapters in in in themselves. Right? Then in thermal properties again you have got many things. So do not miss all of these things. Let's suppose that masses of two liquids are equal. Then directly use this formula. Then directly use this formula for density.

[00:34:37]So you can remember it like this. Okay.

[00:34:39]This is the arithmetic mean. This is can you please write down what type of mean is this? Similar to average speed that we have seen in in chynyatics, right? So you can relate some things. If you have got three liquids fine, you can write it like this. Like for example, as n / d= to one upon d1, one upon d2, one upon d3 and so on. If masses and volumes, see what they are saying. If masses and volumes of two liquids are different, if they are different then you will have to use your normal traditional method that many students are going to apply over here also and they are going to waste their time. So the traditional method is simple that density will be total mass divided by total volume and this is what you're going to get simple right? If masses is also different volumes are also different then simply use total mass upon total volume. If masses are same then use this. If volume are same use this formula directly. Clear?

[00:35:37]Quickly write down in the chat box. And then again relative density is simply density of any liquid divided by density of water. Right? So you're going to use this formula.

[00:35:54]Got it? And relative density for liquid.

[00:35:58]So please remember that all of these formulas are also very important and this is nothing new. Please remember over here W is weight of object weight of object. W A is weight of object in air. WW is weight of object when dipped in water and WL is weight of object when dipped in liquid. Let's understand these formula after learning Archimedes principle. Not learning but let me quickly explain this principle to you.

[00:36:25]The last topic was not that important but please remember our committee's principle is very very very important.

[00:36:32]Almost every year or every uh two year NTA ask a problem from our committee's principle. Right? So this is going to be important in our committee's principle. Simply remember one thing that if we have got a if we have got a body in a liquid singed in liquid or floating in liquid what we are going to say is we have got one force acting downward that is mg that is mg this mg will be balanced if it is floating will be balanced by a bind force.

[00:37:15]And bind force will be the weight of the fluid displaced and that we are going to write down as row l volume of the body time g. Please remember in archimed's principle things will be slightly different if they are going to give something like this. Let's suppose that you have got a container.

[00:37:39]Let's suppose you have got a container and this is a body.

[00:37:44]This is how a body looks like right and this is dipped in some liquid and my dear friends this is actually a hollow body. So we have got mass over here only correct.

[00:38:03]So when we are going to talk about mg for this we are going to write down m into g and instead of mass we are going to write density of the solid times volume of the solid. Now when you are going to write down volume of the solid please remember we are going to only write down this volume.

[00:38:21]Got it right? Hopefully you are getting it what I'm trying to say. So this vdash is going to be different. So we are going to write vdash * g and this and there is one v which is the total volume. Right? So you can understand it like this that let's suppose this is radius R1 and the smaller radius is R2.

[00:38:39]So the complete volume the total volume of the body will be 4 upon 3<unk>i into R1 cube. Whereas Vdash will be 4x3 pi complete volume is R1 cube and the uh this small radius is R2. So this is going to be Vdash. So instead of in mg write down Vdash and when you're going to talk about buant force when you're going to write down the bayant force write down density of the liquid times total volume multiplied by G because water is displaced by the entire body. Quickly write down in the chat box if you are getting it. They have asked a question like this I think in mains in in in recent years. Quickly let me know.

[00:39:26]Clear? So our committee's principle is all done. Also please remember that for apparent weight for apparent weight you can directly use this formula.

[00:39:37]You can directly use this formula my dear friends and you can save a lot of time. Clear? Right. Moving on.

[00:39:47]Law of flotation. If if density of body is greater than density of liquid body sinks.

[00:39:56]Right? If density of body is equals to density of liquid then body just floats and it floats just below the surface.

[00:40:04]Right? And if body of liquid is more than the body of solid or dens sorry uh density of body then it floats partially submerged.

[00:40:17]Partially submerged. So this is law of flotation very easy. The important thing about this law of flotation is finding out the fractional volume of submerged part. Right? Clear the fractional submerged volume. This is important and please mind you if you have got a good hold on archet principle this is very easy but again you can directly remember the formula and and and find the answer.

[00:40:43]I'll tell you what I'm trying to say.

[00:40:45]See when you are going to again talk about mg right when you're going to again talk about mg mass is going to be the total mass when you're going to again write down the mg it's going to be density of solid multiplied by total volume my dear friends so uh this is actually this is v v 1 and v_sub_2 let me call it as v_sub_1 and v_sub_2 this is let's say this is v_sub_1 this is v_sub_2 so v_sub_1 v_sub_2 multiplied by G. Whereas when you're going to talk about bayant force, when you're going to talk about bind force, bind force will be different. Bay force will be or up thrust will be density of liquid multiplied by volume of the liquid displaced that is only this part which is V2 multiplied by G. This is how you are going to do. And because it is floating because it is floating equated. And then you can derive these two formulas relative density of the solid and relative density of the liquid. And the other two formulas is exposed volume divided by total volume and displaced volume divided by total volume. Please remember if you have got basic knowledge of Archimedes principle, you can always derive these formulas.

[00:42:07]But this is going to save a lot of time of yours. Right?

[00:42:12]All right. All right. I'll change the color color of the pen. If you have any doubt, you can ask me. Clear? All right.

[00:42:22]Next is is Newton's law of viscosity.

[00:42:26]Newton's laws of viscosity is again very important when you are going to talk about especially when you are going to talk about terminal velocity or they have also talked about uh units units and dimensions of coefficient of viscosity. Formula is very simple. The viscous force is equals to ea * a into dv by dx where dv by dx is known as velocity gradient.

[00:42:52]This thing is known as velocity gradient. Right? All right. And then EA can be written as my dear friends, EA that is coefficient of viscosity can be written as force divided by area time velocity gradient that is dv by dx.

[00:43:10]Right? So I think now after this if you want to uh write down f / a and dv by da. So you can rewrite coefficient of viscosity in somewhat this way. But most of the time this formula will will help you. Most of the time this formula will help you. I have given you two or more alterations in this formula. For example as instead of dv by dx we have written v by l. Right? If let's suppose v is con if let's suppose put u velocity gradient is constant. So we have simply written as v by l. All right. So and coefficient of viscosity can be also written as shearing stress divided by shearing strain. Right. So after this the most important thing that we are going to use in in using coefficient of viscosity is when a body is when a spherical body is dropped in a fluid.

[00:44:07]When a spherical body is dropped in a fluid we have got mg force acting on it.

[00:44:14]we have got up thrust acting on it or buant force and then we have got also a drag force or a viscous force.

[00:44:27]So these two forces balance mg after some time and at this moment we say that body attains terminal velocity. So remember the formula for terminal velocity.

[00:44:44]This is now important and before that aa please remember the CGS unit of coefficient of viscosity also. I think SI unit is all clear for EA. It will be it will be dying.

[00:44:59]It will be dying per cm squared also called as poise. Right? Got it. And one poisely is called as 10 poise. Although this is not extremely important but please remember it right. They can ask a question from here in units and dimension. Next thing is Stokes's law.

[00:45:16]Again you have to remember this this formula derivation is not given in any book for I mean as far as neat is concerned and this is only for spherical body. This is only for spherical body right where EA is coefficient of viscosity, R is radius and V is velocity. So 6 pi EA RV. So apparent so net force will be apparent weight. Why they are talking about apparent weight?

[00:45:44]Because this is mg minus bind force. So apparent weight minus viscous force.

[00:45:48]Viscous force will always act in the opposite direction to motion. That is drag force. Right?

[00:45:56]After this my dear friends, I have already explained you the concept of terminal velocity. Remember the formula for terminal velocity also. Please remember that terminal velocity depends directly on r².

[00:46:08]Got it?

[00:46:11]Why called as poise? Why called as poise? It is simply a unit. It's simply a unit. There is no other difference. I mean there is no other logic behind it.

[00:46:21]CGS unit is more practical unit. That's why we call that's why we use poise right SI unit is poisely one poisely equals to 10 poise remember this obviously SI unit will be larger unit so its magnitude will be smaller my dear friend right it is the SI unit it is the SI unit so its magnitude will be smaller and its unit is uh the unit is larger so when you're going to talk about CGS unit its number will be large and its unit is smaller correct so remember that One poisly is equals to 10 poise and obviously then you can remember that if it is 10 poise then poise is the CGS unit. Now your doubt is clear. See whenever you're going to ask any doubt in the chat box I'm going to explain it to you. Be be really really attentive over here. These things are important.

[00:47:12]Internal velocity is by the way a favorite topic for NTA.

[00:47:19]Right? So remember this R is R is the radius and V depends directly on the square of radius. If let's suppose they are saying if density of the liquid sorry density of the fluid is greater than the density of the body then the body will attain a terminal velocity in downward direction in downward direction. Clear?

[00:47:42]And if row is less than sigma then terminal velocity will be negative and body will move in the upward direction.

[00:47:51]Got it? And if it is equal then body remains suspended in the fluid. So all the three cases are very very very important. Clear my dear friends. Any more doubts?

[00:48:03]Got it? Done.

[00:48:07]Next is equation of continuity. Equation of continuity. Simply just remember this one thing. A1 V_sub_1 is equals to A2 V2. This is also called as volume flow rate.

[00:48:21]Volume flow rate is going to be constant. Right? Using volume flow rate my dear friends also write down mass flow rate that is dm that is d by dt. So instead of uh mass you can rewrite this thing as density time volume. So density will come out.

[00:48:43]This will be differentiation of volume with respect to t. That means again this is volume flow rate. So volume flow rate was a into v. So we'll get row a into v.

[00:48:55]My dear friends, this v is velocity.

[00:48:58]This v is velocity. Please note this thing's clear. Quickly write down in the chat box. remains suspended means that remains suspended means remains suspended means that you have got a force over here that is mg that we can let's suppose my dear friends oh no problem I I'll explain it to you in the previous slide remains suspended means that you have got a body let's suppose its density is row s and we have got a fluid I'm not talking about simply some liquid. I'm talking about any fluid. Let's suppose we have got a fluid whose density is row L or row F. Clear? Its density is row F.

[00:49:50]Right? That means my dear friend that we'll have an mg over here. Mg will act and this will be the bind force.

[00:49:58]Correct? So instead of mg can I write the volume is V. Got it? volume of the solid is V. So, and this is not in some annular disc type of a thing annular concentric sphere or shell. It is a solid body. Let's assume. So, mg. So, it it will be density of the solid time volume time gravity. Clear? And now over here you will have d u density of the fluid time volume time g. Now they are saying that if let's suppose density of fluid and density of solid are same. If they are same that means bind force will be equals to equals to uh weight right and if bind force will be equals to weight they will cancel out each other and if they will cancel out each other when you are going to when you're going to when you're going to leave a body in this medium the upward force and downward force are same so the body is not going to move if body is not going to move then how come viscous force will come into existence right it is 6 pi ea r into v where r is the radius and v is the velocity. So that means v will be zero. If v is zero that means fv is zero then no viscous force will act. It will not move right.

[00:51:17]See I'm not deliberately I'm not explaining things to you because I am here for only revision. But if you're going to ask me I'll definitely explain.

[00:51:25]Your doubt is clear absolutely sorted right and that is why in this case when they are saying that if row is equals to sigma the body is suspended in the fluid clear can I move on let's quickly move to the to this topic so next one is and just to end this concept let's suppose if I I'll explain the other two also okay let's suppose that this this is greater my dear friend how that will be greater so this was case one. Case two will be let's suppose density of solid is greater than density of fluid density of fluid. Got it? So if density of solid is greater than density of fluid the net force will be in downward direction the net force will be in downward direction. If net force is in downward direction that means I'm so sorry not net force in downward direction. What I'm trying to say is that the the resultant of resultant of mg, resultant of mg and resultant of bind force will be in downward direction and because of this then there will be a drag force or viscous force that will act in upward direction because body is moving down so viscous force will act up and then after some time terminal velocity will be achieved. Got it? Then after some time terminal velocity will be achieved. So this is the body will attain terminal velocity in the downward direction. Got it? And when let's suppose if let's suppose this force is more and this force is less then in that case the body is going up and then viscous force will act down and when viscous force will act down that is why then they are saying that terminal velocity will be negative and body will move in the upward direction. Is it clear? Got it my dear friends?

[00:53:18]Now let's come to equation of continuity. All right. Okay. Good. Good.

[00:53:23]Good. Very good. Very very good. So this is called as mass flow rate. This is called as mass flow rate. This is called as volume flow rate. So please remember equation of continuity is very very important when we are going to talk about when we are going to talk about fluid mechanics. After hydrostatics fluid now the fluid has started to flow.

[00:53:47]fluid dynamics right so equation of continuity if you're going to complete equation of continuity and if you're going to complete uh Bernnoli's theorem most of the questions will be will be covered along with that also cover speed of if flux right got it if you have any doubt you can please ask me I'll answer after this my dear friends after equation of continuity equation of quantity continuity is conservation of mass also remember this and Bernoli's theorem is conservation of energy so the the main uh the main equation of Bernnoli's equation is this that pressure plus/ row v² plus row gh is constant but please remember this pressure is pressure energy per unit volume this is kinetic energy per unit volume and this is potential energy per unit volume also if you are going to actually divide each of these value with ro g then pressure divided by ro g + v ² divided by 2g + ro gh divided by ro g all of these things will become constant and pressure divided by ro g is called as pressure head why it is called as pressure head don't worry don't worry about that but please remember it is called as pressure head and similarly v² by 2g is called as velocity head and h is called as gravitational head got it Clear done.

[00:55:19]Now the condition there are some condition that you must remember before uh applying Bernnoli's principle.

[00:55:26]Although if in a question they are they are expecting us to apply Bernnoli's principle that's fine right? We are going to directly apply it but they can also ask a theoretical question. So please remember that flow should be streamlined.

[00:55:40]Hopefully you remember the definition of streamlined. then it should be non-iscous and that means friction must not act and it is an incompressible fluid right and friction is absent everywhere and also add one more thing into this we are not going to take into account any rotational motion of fluid we are not going to take that also in our into our account right and it is based on the conservation of energy as I have already told you so hopefully everything is clear with this right done clear Write down in the chat box if everything's clear till here.

[00:56:18]Using this using Bernoli's principle we actually derive the formula for speed of flux but derivation is not needed.

[00:56:26]Simply remember the formula and the formula is velocity equals to under root 2 gh. Although actually the formula looks something like this but fine almost every time the size of the hole is going to be is going to be incomparable to the size of the of the top area. That means this let's suppose area of this is capital A. Area of this hole is small A. So we are saying that capital A is far more greater than small A.

[00:56:55]All right. Now I think also do some questions in my class. You know I have solved questions like this that they can also give you problems uh like for example is finding out the minimum friction acting between this tank and the uh floor which will prevent which will prevent sliding of this tank because of this flow of water. If water is flowing, please remember this very important thing that force applied on tank can be also written as my dear friend, it can be also written as v * dm by dt.

[00:57:30]This is Newton's second law when we when we say that velocity is constant and mass is changing. Clear?

[00:57:40]Right?

[00:57:41]Be quick. All right. So again remember that they are they can ask and they have asked these questions in JW mains in previous few years. Simply remember by the way if you know the velocity is equals to <unk>2 <unk>2 gh we can also find out the time of flight my dear friends this this is this is h right this total height is capital h sometimes they also give you this height this is let's say hdash so hdash which will it will be capital h minus small h so time of flight will be under root of 2 h by g so under root of 2 hdash by g if you want to find out This range range will be velocity in x direction that is <unk>2 g into h my dear friends h is hdash uh by the way over here uh sorry h is under root 2 gh multiplied by multiplied by time of flight right multiplied by time of flight let me know if you have any doubt my dear friends uh I'll again repeat this thing this This is very very important. See sometimes what happens that they give tank like this.

[00:58:56]They give tank like this.

[00:59:04]And let's suppose we have got a hole over here, right? And this is this is how the water is filled, right? This this height is negligible.

[00:59:17]So we consider this height to be h. Got it? And this velocity comes out to be v= to under root 2 gh.

[00:59:26]Many times they give a tank like this.

[00:59:29]So do not get confused. We always calculate height from the top to the bottom. So in this case from the top to the from the top to the hole is this.

[00:59:44]So this is small h. So this will be capital H minus small H. Please remember this thing. Is it clear? Be quick.

[00:59:55]Let me know my dear friends.

[00:59:58]Everything sorted.

[01:00:06]Let me know.

[01:00:09]Done. So remember the formula for range also. I mean you don't have to remember the formula for range. Simply remember the formula for V. H is from the top.

[01:00:20]This is one mistake that in neat many students commit. They think that paper is going to be simple, right? And I mean now hopefully from 2025 now nobody thinks that it is simple. But what I'm trying to say is that they remember the formula. They they they remember it.

[01:00:36]They mug it up that okay it's root gh and I'm going to apply it and they write down this as h that will be wrong. Right? So whenever you are remembering any formula whenever you are using a a a formula sheet make sure that you have got a you have got a correct diagram with the formula else formula sheet will make no sense.

[01:00:59]Moving on to now the next topic that is surface tension. So we are right now we are talking only about fluids right so it is combination of all of three things hydrostatic fluids then we have got fluid dynamics and then we have got surface tension part. So surface tension is again force divided by length. We sometimes we write it down as T, sometimes we write it down as S, right?

[01:01:22]SI unit is again Newton per meter. So surface tension and stress, not stress, surface tension and and all the other physical quantities which have got units Newton per meter will also have the same dimensional formula.

[01:01:39]Remember this. And this is going to be dime per cm in CGS unit. Right. Next is surface energy. Simply remember the formula. Surface energy will be work done. Right. Work done in stretching this surface that will be 2 * of T L into X. That basically means we can simply write down surface tension multiplied by change in area. So this is going to be surface energy will be surface energy will be surface tension multiplied by change in area.

[01:02:14]So usually a simple problems comes that we have increased the size of a bubble right all of these things. So please remember to use the formula for surface energy then you have please remember a basic concept that pressure will always be greater on the concave side than on the convex side. So if you have got a drop like this if you have got a drop my dear friends drop has got one surface bubble has got two surface right. So if you have got a drop then always remember that the concave side that means this side will have larger pressure than the outside right concave side will have larger pressure and that access pressure will be written as 2t divided by r that is t is surface tension. Similarly for a bubble there will be two surfaces.

[01:03:01]Please remember bubble has two surfaces one inner surface then one outer surface and in between there is soap solution.

[01:03:08]Got it? In between there is soap solution. So it is four times of tension divided by R and again inside will be greater or concave side will be greater.

[01:03:18]This will be helpful when you are going to talk about capillary rise. So let's suppose you have got capillary tube like this. And let's suppose we have got a surface like this. So what I have told you the concave side will always be at higher pressure. So this if this is A, this is B. So concave side will be at higher pressure.

[01:03:39]Right? And that's why we'll have a capillary rise or a descent in a capillary tube. Got it? Quickly write down in the chat box if all of these things is making sense to you. Please revise like this. And if you if you if you are one time your revision is done, then please use uh things like active recall methods where you have got a plane sheet in front of you. Write down things which you remember from for surface tension.

[01:04:05]Do not go for entire and entire chapters like food fluid mechanics. If you're using active recall for fluid mechanics, divide fluid mechanics into segments.

[01:04:15]Write down everything that you know from the chapter of from the subchapter of surface tension. Write everything that you know from equation of continuity Bernoli's theorem speed of flux. Use three three big topics. Write it down in in a plain sheet in a plain page and then try to recall. Right? So these things are very important my dear friends. Please remember it. Next is is shape of liquid meniscus. It is not they have not asked it a lot but again they can surprise you this time. They can surprise you this time. Please remember it that if they are going to talk about shape of meniscus or they are going to talk about theta write use this formula for cos theta although if you don't want to use this formula you can directly remember the formula for capillary rise that is 2t cos theta divided by row gr the most important thing is if you don't have a diagram with you over here right then nothing makes sense diagram is the most important Think along with diagram please remember capital R is the radius of meniscus and small R is the radius of the tube. If you're remembering the formula and you don't know whether small R is the radius of meniscus or radius of tube you are going to get that question wrong even if you know the correct formula. Got it? So along with formula always when you whenever you are writing down the formula in active recall method write down what those values of R and values of capital R are right clear done all right now let's move to our next chapter that is temperature that is thermal properties of matter right in thermal of properties of matter start with temperature scale hopefully none of you have any doubt in this but do not skip this and for any random scale also we have got a formula over here. So do note this and then again we have got a linear thermal expansion. Use your time effectively. This formula is exactly equal to formula that you are going to learn in current electricity when we are going to talk about temperature dependence of resistance and resistivity. Right? So formula is pretty normal delta L or sorry Ldash will be equals to L * 1 + alpha* delta theta.

[01:06:43]Right?

[01:06:44]And I have already discussed that they can give a a common question of thermal properties along with what? Along with along with our uh Youngs modulus topic, right?

[01:06:59]Using this thing, please remember this very basic and common biometallic strip example.

[01:07:07]See coefficient of temperature coefficient for copper is greater than than iron and that is why it will bend towards iron right it will bend towards iron. So copper will try to bend iron and that is why we are going to have a shape like this. So when temperature increases delta L of copper will be greater than the delta L of iron. Strip with higher value of alpha will be on the convex side. So this is the convex side. Please remember this is the convex side.

[01:07:46]All right, clear. Next is we have talked about linear expansion.

[01:07:53]Now let's talk about superficial expansion. For superficial expansion, please remember that beta can be written as 2 * of alpha. And the equation can be written as a -ash equals to a + 1 + beta * theta. Just remember this, right? We can derive it. Derivation is not needed.

[01:08:11]Right? Now derivation is also very very simple. Right? And obviously every time we are going to talk about isotropic material where alpha value of alpha will not change in different directions.

[01:08:22]Clear my dear friends? And then you have got cubic cubical expansion or volutric expansion. Similarly remember this formula vdash equals to v * 1 + gamma * delta theta. Delta theta is change in temperature and gamma over here will be coefficient of volume expansion. And again we are going to talk about isotropic material. So gamma will be equals to 3 * of alpha. So alpha is to beta is to gamma will be 1 is to 2 is to 3. It's a very basic thing. Clear?

[01:08:52]Everything is clear till this point. Be quick.

[01:08:57]Next is my dear friends applications of linear expansion. In this uh while I was explaining you questions of time period, I have told you this that please remember all the cases for time period of a simple pendulum from each and every chapter. Time period is one single topic which usually comes in in every chapter.

[01:09:20]Right? Starting from units in dimension they they can talk about errors in in in time period formula over here. Please remember what they are trying to say. We have got formula of time period as t = to 2 pi under root l by g under root l by g. Right?

[01:09:41]Now with increase in temperature with if let's suppose delta theta is positive that means with increase in temperature L will increase correct with increase in temperature L will increase if L increases then T increases if T increases then we are going to say that clock runs slow clock runs slow it slows down the simple pendulum slows down. Right? So this is very important. When temperature increases, time period increases and that means clock runs slow.

[01:10:23]Similarly, when temperature decreases, time period decreases and that means clock runs fast. And loss of this is again very very important formula.

[01:10:34]Please remember it. The loss of time in any given interval simply write it down as this 1 upon 2 alpha * delta theta multiplied by t. 1 upon 2 alpha into delta theta multiplied by t. Right? So time lost by a clock in a day. We know what this t is. This t is going to be 86,400 seconds. Please remember this. Please remember this. This is the uh seconds in a day.

[01:11:07]Now please try to understand why this formula sheet is very important. If you already know that okay fine sir in in one complete day we have got 86,400 seconds then you can save a lot of time.

[01:11:18]Clear? All right. So time lost in a day is also sorted. Now let's move on.

[01:11:26]Hopefully this is all good. And now let's talk about heat supplied the next portion of this chapter. Right?

[01:11:35]Got it? So if let's suppose you're supplying heat to a body and its temperature changes. So you are going to use this formula delta Q= to MS delta T.

[01:11:51]Q equals to the amount of heat supplied is equals to mass multiplied by specific heat multiplied by delta T right and the SI unit is going to be joule per kg per kelvin remember the SI units of these things it is also very important as as well as for water please remember that the unit is 1 calorie per g per°C right and also I'm going to write it down over here 1 calorie is actually equals to 4.18 Jew Jew or you can rewrite this thing as 4.2 ghou 4.2 2 ghou. All right.

[01:12:30]So remember the specific heat capacity for water, for ice and for steam, right?

[01:12:36]Even if they are going to give it to you, fine. But please remember it and I'm going to help you in the unit also.

[01:12:41]So the basic reference is that we have chosen the value of water as one. So remember it like this that reference is water. So for water it is 1 calorie per g per deg. If you want to just convert calorie into jewels and want to keep all the units in as same. So one will be changed to 4.2 Jew divided by g by g per degree. Now let's suppose you want to convert g into kilog then 1 g is 10 ^ minus 3. So it will become 10 ^ 3 in the numerator. That means 4200 jou per kilogram per deg.

[01:13:19]Next thing is my dear friend let's suppose you want to write it down in kilojoule right so you can write it down in kilogjle as again 4.2 2 into kiloj per kilogram per deg right and then for ice simply remember that for ice it is half of water that is 1 upon 2 calorie per gram and then you can again rewrite it everything is clear my dear friends so kilogram please remember the unit as kilojoule per kilogram deg joule per g per degree or calorie per g per degree got it usually what you're going to use is you're going to either use calorie per g°C CC or you are going to use kilojoule per kilogram deg.

[01:14:02]In either ways please try to convert it.

[01:14:04]Conversion is not very difficult. The reference should be clear in your head.

[01:14:08]That is 1 calorie per g per degree. We are never going to change degrees. So either we are going to talk about gram or kilogram or we can convert one calorie into one joule.

[01:14:22]One calorie into joule not one. Now if you are not just changing the temperature you are also changing the state of the body then we are going to also talk about latent heat of vaporization and latent heat of fusion.

[01:14:35]For that my dear friends first talk about melting. If if state is changing obviously you cannot use this formula because during the change of state delta t remains constant and all the heat that we supply into a body is used to change the state of the body. It does not it does not change the kinetic energy of the molecule. That means temperature does not increases increases. Remember this thing right? So delta Q will be equals to M * L and L over here is latent heat of fusion. Please remember whenever we are going to talk about melting for example from ice to water you are going to use latent heat of fusion and the value of latent heat of fusion is 80 calorie per gram. Please remember that most likely they will give you values like latent heat of fusion and latent heat of vaporization but do not take risk and also do if you if you are thinking sir now exam is just after a week and we have we can't remember new and new uh data so simply remember one values this is all clear this is one this is one 0.5 1 by 2 please remember this thing has 80 calorie per gram and this thing has 540 calorie per gram that is latent heat of vaporization and then we can convert it in exam if there is any need got it if you don't already remember these formulas right and then next one is boiling so boiling is again going to be m into l is everything clearly let me know let's suppose if I've got 1 kilogram of of ice and I want to convert it into 1 kilogram of water then how much heat is required I can get it from here be quick Right, it's done.

[01:16:32]Can we move on?

[01:16:37]Now comes this curve.

[01:16:40]My dear friends, let's suppose that we have got a ice.

[01:16:44]We have got some ice over here of mass of mass right at let's suppose at 0°C or let's suppose at some degus 10°C. So first and what we are doing is using some heater or something like this.

[01:17:15]This dq by dt is constant. So this is actually rate at which heat is supplied.

[01:17:22]This is constant. dq by dt is constant.

[01:17:25]Got it? So if dq by dt is constant first this ice temperature will increase and it will get increased to 0°C and at 0°C we will get a mixture of water and ice.

[01:17:41]We will get a mixture of water and ice and then heat is we are constantly supplying heat and then this will get converted into 100% water but temperature will remain same my dear friend temperature will remain same then we are going to increase its temperature and let's suppose we are increasing its temperature to 100°C. So at 100°C it will be water plus steam and then again we'll convert it into 100% steam and again that will be at 100°C and then again if you want to again increase its temperature to let's suppose 140°C so it will be 140°C and it will be completely steamed. So what is the total amount of energy required? So simply do this. This is Q1 and this is going to be mass specific heat of ice time deltat T. This is going to be delta Q2 and this sorry Q2 and this is going to be mass time latent heat of fusion.

[01:18:42]This is Q3 equals to mass time specific heat of water* delta T. And this is going to be Q4. This is going to be mass time latent heat of vaporization. And this is going to be Q5. And this is going to be mass time specific heat of steam time delta t. Got it my dear friends? Everything's clear. So this is how you are going to find out the total energy required from ice to a particular point. Please remember do not directly use these formulas. When we have got a question of mixing of two things then question becomes slightly difficult. All of my students remember how to solve those questions. We are going to talk about those. I mean I'm using my terminology so it's not some bookish language. We are going to talk about uh deficit in energy and access in energy and then we are going to find out whether we have got ice left, water left or steam. Right? So that is a completely different topic and question. So my point is this dq by dt is constant. So that means slope is constant. So ms t1 divided by t1 mlf divided by change in time. This is change in time my dear friends. So this Q byt is going to be constant for each of them. And this is how the graph will look like. Any more doubts my dear friends? Clear, sorted, be quick.

[01:20:06]Right?

[01:20:09]You guys are understanding right what I'm trying to say about those mixing question. Let's suppose that 1 kg of ice is mixed with some gram of water at at so and so temperature. So you cannot apply this formula over there right and how to do that let's not get into it my students know it I have explained that in in class that is slightly difficult on on difficult side so if you don't know that right now you can skip it you can skip it it's not like very important for neat exam then my dear friends you have got two simple uh formula not formula definitions one is heat capacity and one is water equivalent Please remember heat capacity simply now we know what is specific heat capacity. By the way I have not defined it but hopefully I I can trust that most of you know what heat cap what specific heat capacity is. So for finding out heat capacity simply multiply mass with specific heat capacity you will get heat capacity. Got it? So mass multiplied by specific heat capacity is normal heat capacity. And obviously now we are cancel we'll cancel down the unit of mass. So we'll be left with calorie per calorie per degree CC or calorie per kelvin. Got it?

[01:21:26]Done.

[01:21:28]And for water equivalent the mass of water that will absorb or lose the same quantity of heat as given substance will do for same change in temperature.

[01:21:38]Right? So this is called as water equivalent. And this is the formula for water equivalent my dear friends. All right. the the mass of water that will absorb or lose same quantity of heat.

[01:21:54]Now the next part and the last part that is heat transfer for heat transfer my dear friends conduction is again important. Let me also tell you why I'm saying this is important because last year also they have asked a question from conduction right. So conduction is important.

[01:22:14]So and along with its importance it is also similar exactly similar to current electricity. Please remember this formula. This is again dq by dt my dear friends and do not get confused with the unit dq by dt basically means that right now we are talking about what power is what right? K is a constant.

[01:22:40]K is a constant and A is area and again D theta by DT DX is temperature gradient.

[01:22:50]Temperature gradient. And uh I believe my dear friends there is a small error in this. Can you guys write down that that error in the chat box?

[01:23:00]Can you write down that error in the chat box? What is the small error we have got over here?

[01:23:08]There's a error in this sir. Can we define heat capacity is rate of change of heat? No, no frame.

[01:23:27]It's not rate of heat of change with respect to temperature.

[01:23:35]First tell me the sir will there be cast? Absolutely there will be. There will be we have got a negative sign over here. I mean we should have a negative sign over here right and because of that what we are going to write is that delta q divided by deltat t this is time is equals to minus k a higher temp uh sorry lower temperature minus higher temperature divided by l let me explain it to you if you have any doubt see why I'm explaining some things why I have explained argument principle in detail why I have explained viscosity in detail why I have explained change of state in detail for a simple reason that I have seen that more questions comes from these topics so you can also pay some attention let's suppose that we have got a rod like this and we have got two reservoirs over here one is a a colder reservoir and one is the hotter reservoir right that is how we draw diagram so this is lower temperature this is higher temperature uh sorry let's say this is higher temperature and this is lower temperature correct so heat travels in this direction heat travels in this direction and if heat travels in this direction so the rate of flow of heat will be directly proportional to area it will be directly proportional to temperature gradient so that is why we are writing final temperature that is TL minus TH but obviously this will come out as a negative this will come this will be a negative thing. So that is why we have we have also applied a negative sign over here. So finally this formula will actually become finally this formula will become something like this K A by L and that is TH minus TL. Please remember this formula. And after this also remember that we can now write this dq by dt as heat current.

[01:25:44]dq by dt as heat current. And we can write it down as t h minus t l divided by k a l divided by ka. So this is analous to to current electricity. And similarly this is called as heat current.

[01:26:04]This is called as heat current. They have asked a same question in 2025. By the way, this is known as temperature difference which is analogous to potential difference. Is that correct?

[01:26:19]And this is known as resistance.

[01:26:23]Resistance of the rod.

[01:26:25]This is known as L divided by K where K is a constant, right? Which plays the role of of conductivity in this case. Is everything clear my dear friends? Let me know. So in series combination current will be same. In parall combination temperature difference will be same just like current electricity no difference.

[01:26:45]Right? So moving on please see I have explained each and everything to you.

[01:26:50]Heat current is dq by dt. H is equals to theta1 divided theta 1 minus theta_2 divided by 2. Please remember theta 1 is more that means higher temperature.

[01:26:58]Right? And thermal resistance is l / k.

[01:27:02]That that is how you write down heat current. Clear? Series combination current will be same parall combination potential difference in this case temperature difference will be same. And then you can see series combination like this. So whenever you have got series combination right. So please remember heat current from here to here and heat current over here and heat current between any two section will be same. So this is how we solved the question of need 2025. If you remember, so this is see this is higher temperature this is lower temperature then this is higher temperature this is lower temperature then this is higher temperature this is lower temperature what I'm trying to say is for every section higher temperature will be on this side and lower temperature will be on this side because this is the direction of heat current always goes from higher potential to lower potential so heat current also goes from higher temperature to lower temperature so when you want to write down current, you can write down current between these two things, between these two things and so on. Hopefully everything is clear. Mark this thing as important. Clear? Moving on to the next one. Similarly, my dear friends, then you have got parall combination. In parallel combination, this side has temperature theta_1, this side has temperature theta_2. So, temperature difference is same. Heat current is different. So, total heat current will be I1, I2, I3 and so on. I in. So this is the this is how you can write down the combination of resistances. Exactly the same thing that we do in current electricity.

[01:28:39]No difference. Right? So I mean now again many students actually skip transfer because they think that thermal properties of heat is a single chapter.

[01:28:49]It is not a single chapter.

[01:28:53]Conduction is different. Then you have got uh you have got then specific heat part and then you have got heat transfer part right and then we have got conduction and convection uh sorry then we have got convection and radiation you can skip radiation if you want many parts of radiation is deleted you can skip that if you want but no one knows if they can ask anything from the deleted part as well right so we can't be sure now my dear friends let's quickly complete KTG and thermodynamics then I'm going to include the waves part in class 12 because I'm going to include SHM waves alternating current EM wave and wave optics in a single sheet right so let me also give you notes of uh thermodynamics and uh KTG that will complete your class 11th 95% of the things please remember for waves and for SHM I'm going to club these two things with alternating current wave optics and EM waves is is it clear quickly write down in the chat box.

[01:29:57]Now again thermodynamics and KTG is a thing which which which large portion of these things converges with chemistry also. I'm I'm going to in this class I'm going to again uh highlight the difference between thermodynamics in chemistry and physics and then we'll end the session. My dear friends, please remember the degree of freedoms of these things. That is very important. You know that we we are going to use degree of freedom in in in further calculations.

[01:30:23]Please remember specific heat. All of these formulas are very basic, very important in thermodynamics also. That is CP by CV.

[01:30:32]CP by CV is equals to R. CP minus CV is equals to R by M. Right?

[01:30:39]Got it. Specific heat per unit mass.

[01:30:42]Then for mono, dia and tri remember the value for of gamma. And also in terms of gamma please remember the formulas of CP and CV. All of these things are very easy to convert from one formula to another. But you must remember it. I think is some in some previous year they have given a very simple problem related to this thing related to this formula.

[01:31:09]Right? So do this thing. Then mixing of gases again just like mixing of liquids. Remember the formula of mixing of gases and that is very simple.

[01:31:20]CV will be N C1 N CV1 + N_sub_2 CV2 and so on divided by total number of moles.

[01:31:28]If you want to write uh the value of CP for the mixture, it would be N1 CP1 plus N_sub_2 CP2 and so on divided by N was plus N_sub_2 and gamma will be again the same formula that we have just now seen and you already know that is CP mix divided by CV mix. So for gamma have we written gamma over here but you know now gamma is CP by CV. If you have not written over here, let's write it down that gamma is CP by CV.

[01:31:58]Right? Clear.

[01:32:00]Be quick.

[01:32:03]Yes. This is going to help you in adiabatic process also. Exactly.

[01:32:10]Then my dear friends, law of equipartition of energy and energy. This is actually now important because many times students get confused in sir whether it is f_x2 kt fx2 nrt what is the correct formula. This one page will help you a lot. Please remember that energy for each molecule per degree of freedom is 1x2 KT and this is law of equipartition. Got it? This is law of equipartition.

[01:32:38]That means total energy for a molecule will be multiply the total degree of freedom that that means it will be FX2 into KT right and K is Bzman constant that's why they are writing KB for more atomic write down the formula of F that is three for total energy of 1 mole now this is very important for one mole it would be FX2 into RT got it will be FX2 into RT for n number of moles it would be FX2 into NRT Let me know if you have got any doubt and this is how later on we are going to write down our formula of deltaU also is it clear sorted my dear friends other than that mono diatomic and translatory kindinetic energy this thing should be all clear again this is very important for comparison RMS average and most probable uh remember it you don't have to derive it although RMS RMS is derived using the same things as we are going to use RMS in other places. So RMS is under root of 3 RT by M. This is 8 RT by PM and this is 2 RT by M. At least remember the order in which these uh they happen to be right. So the most uh the greatest velocity is of average 1 sorry greatest is of RMS of course 1.225 225 then comes average 1.13 and then most probable that is one clear so remember the order remember the basic formula as well and then this is not that important but please remember the formula that is mean free path this is exactly the mean free path that we talk about in I mean uh similar concept that we talk about in drift velocity so this is also mean free path that is average distance traveled by molecules between two successive collision collisions over there we talk about relaxation time time taken by the uh by the electron between two collisions. Got it? Clear right?

[01:34:44]So remember this formula also derivation is not given in your course formula is important. And then this is something that I was talking about that is internal energy. My dear friends internal energy is given by deltaU is given by NCV delta t. Please remember it has got to do nothing with constant volume. It happens to be the same formula. We are not talking about some process or we are not talking about any specific case. It happens to be that formula comes out to be nfx2 nrt and we know that cv can be written as fx2 into r and that's why we are simply using it as ncv delta t. Got it? We are not talking about isocoric process. Internal energy formula is NCB delta T.

[01:35:34]Now collision all of these things are not important.

[01:35:38]Huh? In mains if things mains mains happens in I mean for a month and it happens every day in different shifts if something is out of your course do not waste time in especially in those things right you solve main's problems but do not go for these topics which are not important in need all right this is very important so fx2 nr delta t now please remember wherever you are going to talk about n R delta T you can always use PV is equals to NRT I'm sorry you can always use PV equals to NRT for for gases for ideal gases. So instead of N R deltat T N R delta T you can write down delta PV or you can write down P1 V_sub1 equals to P2 V2 got it right. So instead of this you can write down P2 V2 minus P1 V1 divided by gamma minus 1. So internal energy is only function of the temperature of the gas. This is also very very important. Why? I'll let you know. See using this. Now I'm going to give you a entire revision of thermodynamics. Entire revision of thermodynamics. Just stick with me for some more time. This is the point that I was saying we are going to talk about first in thermodynamics that is sign convention. The only difference in chemistry and in physics when we are talking about thermodynamics is of sign convention. Please remember whenever we are going to do work on the gas if work is done on the gas if there is compression remember it like this.

[01:37:18]Remember it like this my dear friends that for us work done is P into DV.

[01:37:25]This is work done right? P DV. Now PDV can be also you can also consider like we have got a system if gas is expanding that means volume is going to increase if volume is going to increase that means work will be positive for us it is a mathematical equation for now let's assume right so this will be this will be positive in only one case when you have got initial is greater than final when upper limit is more that means there is an expansion so when you are going to talk about compression you're going to write down a negative sign, right? And when expansion is done, that means work done by the gas. Gas is doing work. If we will do work on the gas, that will be negative sign. If gas is doing work, that will be a positive sign. If you are giving heat to the system that is positive. If we are deriving heat from the system that is negative.

[01:38:24]Got it? So this is first law of thermodynamics my dear friends.

[01:38:30]To give you a quick revision of first law also you can understand something like this. Let's suppose you have got a piston over here and we have connected a heating element right and using this heating element we are actually supplying heat to this system. So you are supplying heat and then this heat can be utilized.

[01:39:00]Please remember like this. If any student has any doubt in thermodynamic first law of thermodynamics, please remember it like this. This heat will be utilized in two ways. First to increase the internal energy of the system as you know internal energies is written as n fx2 r delta t. Correct? So if let's suppose temperature increases that means deltaU increases. So if you are giving heat deltat t it may increase. I'm not saying it will increase it may increase. Right?

[01:39:30]Don't say what about if it is an isothermal process. Let's not talk about processes right now. I'm saying that heat can be utilized to increase the internal energy of a system. Plus this piston can move in this direction. That means we can do some work.

[01:39:52]That means gas can do some work. Right?

[01:39:54]Using this heat, gas can do some work.

[01:39:57]So this is how you can write it down.

[01:40:00]And this is why you have got QP= to deltaU plus delta W. DeltaU is my dear friends, deltaU is FX2 NR delta T or N CV delta T. CV delta T, right? It is just you please remember we are not talking about isoporic process. It is just by a fluke that that formula is same as CV right. So NCV delta T and we know work done is P DV remember these two things and then after that we can talk about everything else.

[01:40:32]Next important thing my dear friends.

[01:40:37]All right Prem now everything's clear my dear friend.

[01:40:44]Now everything's clear. Good. Now first law of thermodynamics is clear. Now the next thing is please remember which things are path function. That means they depend upon the path and which are path independent. Right? Which are state function. State function basically means that they only depend upon the final variable. What I'm trying to say is let's suppose you're you're changing the variables of a gas from state A to state B. Now state A has temp pressure P1 volume V_sub_1 temperature T_1. This has variable pressure P2 volume V_sub_2 temperature TS2. Right? So what I'm trying to say is that temperature is T1 and temperature is T2. That means no matter from where you go from which from which path you take what process you take final temperature is t2 right so finally potential energy will be finally potential energy will sorry finally I'm talking about potential energy potential energy is zero we only talk about kinetic energy component finally internal energy will be because internal energy is is related with kinetic energy if internal energy is more that means kinetic energy of molecules is more So what I'm trying to say is that if if temperature is t2 internal energy will be fx2 nr deltat t got it so delta t basically means t2 minus t1 ts2 minus t1 got it t2 minus t1 so no matter from where you go delta u will be same but that doesn't mean that q1 will be same or w will be same w depends upon the path whether we are talking about isocoric process or isothermal process process or adabetic process work done will be different. Is that clear?

[01:42:39]Average is 3x2 KT my dear friend.

[01:42:42]Average is 3x2 KT.

[01:42:47]See pre I I'll I make you understand one thing my dear friend. I'll go back for you. If you're talking about each molecule per degree of freedom buddy pre if you're talking about per degree of freedom then you don't have any f on the right hand side. Now if you are talking about for a molecule then you have got f over here. Got it? So it is very simple. Now you now you'll have no doubt in this.

[01:43:20]Hopefully this is all clear.

[01:43:26]And then my dear friends then you have got heat. Heat formula is n c delta t.

[01:43:32]And then for adiabetic process delta q will be zero. Of course no heat rates transferred at constant volume we are going to write ncv delta t and at constant pressure we are going to write delta u plus delta w and in that case it will be ncp delta t right. So delta plus w is equals to ncp delta t that is q. So q q is the formula for q is simply n c delta t right and then we can write it as ncv delta t at constant volume. The reason for constant volume is that at this work done will be zero.

[01:44:11]So using first law simply qv= to delta u and that is ncv delta t. Now at constant pressure this will be p qp= to delta u plus delta w and that will be ncp delta t. Hopefully this is all clear and also please remember that it is area under the curve. Work done is area under the curve. Okay. Glad glad buddy.

[01:44:40]Now next thing is remember all of these graphs. Right. So after I'll upload this sheet. In this sheet you will get almost everything which are highly important.

[01:44:52]One or two things you might think that okay this is missing but almost all formula I've got over here for isobaric process of course work done is pressure multiplied by V_sub_2 minus V_sub_1 area under the curve for isocoric process work done will be zero right volume does not change for this process my dear friends find out the area between this path that's going to be this area and then this path this whole path and then subtract it. So you'll get down the you'll get the area of this closed path right similarly for this and this right this is what we are trying to do first for AB this is w1 and then for this that is w2 and we can see that w1 is greater than w2 got it clear my dear friends next is expansion remember the graph for expansion uh this is very important as you guys know for Isocoric it is zero. Then comes adiabetic. Then comes isothermal and then comes isobaric. Right? So remember this order also.

[01:46:10]Remember this order also. Clear? Done.

[01:46:18]For compression similar order will be something like this.

[01:46:25]Although compression is that not that much popular, not that much important but do remember it. If you're going to simply reverse it, you're going to get to compression, right? And in compression, why we are talking about the modulus values? Because work done will be negative in compression.

[01:46:42]For cyclic process, my dear friends, whatever is the the area which is inside the graph is known as work done. I have given you one case. So for this one area will be 1<unk> by 4 * p2 - v_sub1 * r v2 - v1. Please remember this formula. This is very important. It is area of ellipse if you remember. Right? And for this one it's going to be simply half base into height. This is very easy. Please remember the area for that one. Got it?

[01:47:14]Clear?

[01:47:17]For clockwise work done will be negative. For anticlockwise work done will be positive. So this is also one very uh common con it's not convention it makes sense if it is clockwise then it's compression it if it is anticlockwise that means its expansion and work done will be positive clear that's it my dear friends we are also almost done remember the this is also really simple it's a uh rectangle so it's going to be p2 - p1 * v2us v_sub_1 and this is anticlockwise so this is positive that is expansion Last few formulas for you. Remember formula for adiabetic. We already know that for adiabetic Q will be zero. No exchange of heat. That means delta U will be equals to negative * of delta W.

[01:48:06]And we know what deltaU is, right? So if temperature increases, deltaU is positive. And if delta U is positive, that means work is negative. Clear? So in expansion, work done will be negative.

[01:48:20]And no uh just a second in compression work done will be negative in expansion this will be positive right this will be positive and this will be negative I think there is some mistake we have corrected it clear so deltaU decreases temperature decreases pressure decreases hopefully this is all clear in expansion always work done will be positive so no doubt about it then my dear Friends, please remember these equation. This is for adiabetic PV= to gamma= to constant and using other equations like for example as P can be written as N RT / V. That means instead of P you can write down T / V.

[01:49:09]So write T / V.

[01:49:13]T / V * V raised to the power gamma is equals to constant. That means t v raised to the power gamma minus 1 is equals to constant right and similarly now you can convert you can rewrite v in terms of t. So you can have p and t right. So you can have p and t and this is the formula for work done in adiabetic process. Remember uh this is p1 v_sub1 minus p2 v2 divided by gamma minus1. All right do note this also. And in isothermal the most important formula is this which is if you don't want to write down in in in this 2.303 format then you can simply write down nrt natural log v2 upon v_sub1. Please remember that natural [clears throat] log can be written as 2.303 into log to the base 10. So this is log to the base 10. So uh last is isobaric process and isocoric process. So we all know for isocoric isocoric process isocoric process delta v is zero so is delta w0 right and for isobaric process pressure does not change and that means if pressure does not change q can be written as delta u plus delta w and finally we can write down work done as p * delta v or n r delta t so this is also simple right other than this cv formula cp formula All are similar. That's what I was saying at the start of KTG.

[01:50:45]Remember all the formulas of CP, all the formulas of C, CV. That will help you a lot. Clear? So after this now, we are going to continue from our next life class and in that next life class I'll take class 12th. In that I'll club SHM and waves also. All right. So this was till your class 11th. Now we are going to end today's class.

[01:51:09]All right, done. Okay, then see you in in our next class. Those bye-bye. Thank you so much.

[01:51:21]Okay, bye. Bye. Bye. Bye.

[01:51:24]Bye-bye.

[01:51:27]Notification for next class will be uploaded on this same channel. Okay, bye. Thank you so much. Bye-bye. Bye.