This lecture provides a clear and mathematically rigorous foundation for understanding thermodynamic properties and temperature scales. It effectively bridges the gap between abstract physical concepts and practical exam-oriented applications.
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Deep Dive
HEAT | 2027 A/L | English MediumAdded:
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So what I was talking was usually this starts at 7:30 but it would usually move until 7:45 cuz it entirely depends on when we finish the first class. That means we have a class ending at 7:30. So if it moves to 7:35 you would usually start this around 7:45. Okay. So let's keep the time as 7:45. Okay. Let's keep the time as 7:45.
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Okay. So let's start the heat lesson. So when starting the heat lesson, we have to talk with we have to start with something we already know. Pay attention. We have to start with something we already know that is temperature.
Temperature. So we start the lesson with the term called temperature. Pay attention everyone.
Okay. We start this with the term called temperature. So what is temperature?
Uh it's just a kind of sense, right? Pay attention. Stop talking.
It's a kind of sense that something we feel when you I mean like it's not heat. Heat is a type of energy.
Okay, heat is a type of energy that you already know measured in jewels. But how do we understand heat? We understand heat by temperature. Right? Clear? What we feel is temperature going up and down. Okay. So, what is this temperature? What is this temperature?
Temperature is actually the kinetic energy of the particles. Okay.
Temperature means the kinetic energy of the particles. Okay. Kinetic energy of the particles of a system.
That means a system is made of particles like this. Okay. System is made of particles like this. Okay.
Then all these particles will have a certain oscillation. Right? I mean although we can't see that okay although we can we can't see that all the particles have a certain oscillation.
Clear? All the particles of anything have a certain oscillation and a certain oscillation frequency. Okay? That means a certain vibration. Clear?
All the particles in any system has a certain vibration. Okay? Uh this vibrational kinetic energy is what we feel as temperature. Okay? That means when you touch something, okay, if this is your finger, okay, you have particles on your finger. So what happens is these oscillations, these oscillations start oscillating these particles. Okay, these oscillations, these o vibrations, they start triggering other particles.
Clear? They start triggering other particles. Clear? Then oscillations start to continue. Okay. Then oscillations start to continue. Clear?
Oscillations move forward. Clear?
Oscillations move forward. Okay. Uh that's what we feel as a temperature.
Okay. Clear. That's what we feel as a temperature. So ideally uh temperature is the vibrational kinetic energy. Okay. Temperature is the vibrational kinetic energy of the particles of a system. Got the idea?
Okay. So one line students hope you have the tooth right only.
Hope you have the tooth. You can find the tooth in the drive. Okay. You can there's a drive link avail the tooth for most of the students.
Okay, clear.
We have delivered the tooth for most of the students. Uh but I'll give information again to get the tooth delivered.
Uh so for now if you don't have the tute with you you need only tute one heat tute one that you can find in the drive link available in the live chat and in the zoom webinar resources and again it's available in your groups too. Okay it's available in your groups too. Okay so to start with to start with to start the heat lesson we are going to learn the zero law of thermodynamics. Okay to start the heat lesson we are going to learn the zero law of thermodynamics 90% of the content is available in your book but today we today and the next day we may have to write a small part after that everything is available on your t okay initially a small part has to be written okay so pay attention now uh what is the zero law of thermodynamic and why why Don't we have the first law of thermodynamic? Why do we have a zeroth law of ther thermodynamic? Uh the reason is actually the first law was initially found. Okay. And not the zeroth law the much fundamental law was discovered later. Okay. So the zeroth law this zero law of thermodynamics is extremely simple. It's simple such that I mean we can't even understand why do we have a law like that. It is um like let's take this system as B, this system as A and this system as C. We are telling that if A and B is in thermodynamic equilibrium, if B and C is in thermodynamic equilibrium, then definitely A and C should be in thermodynamic equilibrium.
What is this thermal equilibrium or thermodynamic equilibrium?
It is the particle movement is matched.
That means if uh if this system has a certain kinetic energy, particles has a certain vibration which means a temperature.
If the system next to that has the same kinetic energy, same vibration, which means the same temperature, then the particles will move together. Right? No kinetic energy will be transferred from this guy to this guy or this guy to this guy. Right? No kinetic energy will be transferred. Right? So this is what we call a thermodynamic equilibrium.
Basically they have same temperature.
Okay? Clear? Basically that means they have the same temperature. Okay. So the simplified version of this is if these two are in the same temperature, if these two are in the same temperature, then these two must be in the same temperature. Okay. Clear? Why do you need an equation like this? Cuz when it comes to any physics law, everything should be defined. Okay, clear? That means uh without a electrical potential difference, without electrical potential difference, electrons will not flow.
Okay, that's why we need batteries.
Without electrical potential difference, electrons will not flow. That's why we need batteries. Like that a similar statement is this. Okay. If no heat flow, if these two are in thermodynamic equilibrium, that means if these two have the same temperature, there won't be any heat flow between them. If these two are in thermodynamic equilibrium, that means if they are in the same temperature, there won't be any heat flow between them. Then there won't be any heat flow between these two points either. Clear? Okay. Clear. So it is a much fundamental law that we anyways understand by common sense. Right?
Clear. A much fundamental law that we understand by common sense. But it's okay. Clear? Cuz we have to learn things from the fundamentals. Clear? Okay. So moving forward.
Moving forward. Since we started with the topic temperature.
Since we started with the topic temperature.
Uh since we started with the topic temperature, we are going to talk today about measuring temperatures. Okay. Clear?
Today we are going to talk about measuring temperatures. Okay. So, uh talking about measuring temperatures, uh like I mean although the lesson is heat, we are going to talk about heat much later. Okay? Cuz we first should have a proper understanding about temperature cuz that's how we are going to understand heat, right? Whether heat should flow, whether should I mean whether will it flow or not and everything or clear? Ah, so the methods we are going to me use to measure temperature are thermometric properties.
Okay.
The methods we are going to measure temperature. So today we are going to discuss about a very simple topic. It's about measuring temperature. Okay. Okay, these things you have even had in all levels. Okay, so today's topic is measuring temperature. Okay, so talking about measuring temperature, uh we use thermometric properties to measure temperature. What are thermometric properties? Thermometric properties are the properties that changes with temperature. Okay, thermometric properties are properties that changes with temperature. Okay. Any property cuz temperature you can't see.
Okay. So you need a different mechanism to measure temperature and that different mechanism is usually a certain physical quantity that connected with temperature. For an example expansion of something you know that the mercury thermometer there what happens is mercury expands and that expansion indicates temperature differences. Okay that expansion indicates temperature differences.
That's what we understand right clear.
Then there are some um some some other physical quantities that can change with temperature such as pressure, volume of something uh and at the same time in certain scenarios uh it is the current flow sometimes the resistance changes with temperature. Clear there are different uh physical quantities that we can understand and at the same time they changes with the temperature. So we use them to measure the temperature. Okay. Cuz the measure temperature cannot be measured directly. Okay. Clear? Ah. So talking about these thermometric properties. Okay. Talking about these thermometric properties. There are two main thermometric two main uh characteristics.
Okay. There are two main characteristics that thermometric properties should follow. Okay. If you don't have to request from inulators. Okay. Um there are two main characteristics that thermometric properties should follow.
They are one is these thermometric properties should be one to one. Okay.
The thermometric properties should be one one or single valued functions.
Okay. They should be one one or single valued functions. That means I mean if I'm using something to measure the temperature if this is the temperature if this is that property okay it shouldn't be like this okay it shouldn't be like this why why is the reason the reason is uh like if this is the property if this is the property if that property predict two temperature possibilities. Okay, if that property predicts two possible temperatures. Okay, if that property predicts two different temperatures, I can't directly tell the temperature.
Right? Clear? I can't directly tell the temperature using that property. Right?
It may be the electromotive force or current. When current is 5 ampers, if there are two possible temperature values, I can't do anything about that, right? Because I then I have to assume.
Okay? So this is not good to measure temperature. So if we are using a certain property to measure temperature that property should be like this a one one function. Okay. So you exactly know at this property value this is the temperature you exactly know at this property value this is the temperature like that then you have a proper idea about what is happening. Clear? And the next must is having a continuous property. property should be continuous.
What is that? That means if the property is like this for every property value you have a temperature. Okay, clear.
Your this can cannot be discontinuous like this. Clear? The property cannot be discontinuous like this. Clear? There can't be certain jumps in between. Okay. Why? For obvious reasons.
For obvious reasons, you can't create a proper scale, right? You can't create a proper scale using something like this, right? Okay. I mean, if you are using a property like this, then in your thermometer, assume you have a mercury thermometer, you will have to mark temperature values like this. Then again like this, okay, which is not convenient, right? Okay.
You can't have sudden jumps. That means your like the property cannot be Your property cannot be missing missing at certain temperature values. Okay?
There cannot be any breaks. Okay?
There cannot be any breaks in the middle. Okay? It should be continuous.
Clear? Okay? Got the idea? It should be continuous.
Then what are the other characteristics?
What what are the other good characteristics? That means this is a must. If a certain characteristic does not follow these two, we cannot use that. Otherwise, we can. But there are some characteristics that we prefer.
Okay. There are some characteristics that we prefer to have. What are they?
Um, one characteristic is linear variation.
What is linear variation?
Linear variation means linear variation of a property means I mean if you have a variation like this this is the temperature this is the property it follows everything okay it follows everything it follows the all the basic rules if you have a property like this still follows all the rules okay still follows all the rules but what what is the problem it's really difficult to mark a scale right using this right I mean when you mark the scale on your thermometer you may have to mark it like this very random right clear if it is not like if it is not linear okay if it is not linear it's really difficult to mark the scale right okay okay I mean if your property is right this if your property is perfect like this okay then you would have a very linear scale marked on your thermometer. Very easy to read. Okay.
Very easy to read. Very easy to manufacture. Very easy to predict temperature values given the property.
Right? Clear. So linearity. Okay. And the next this is not a must by the way.
Why? Somehow you can create a working thermometer. Right? Even like this somehow you can create a working thermometer but not very good. Right?
Okay. And the next thing is having a huge range. Okay. having a huge range.
Why? Obviously, if if there's a huge range, you can work you you can use that thermometer, okay, to measure a lot of things, right?
So, having a good range, not a must.
Okay? In certain scenarios, there are thermometers that specifically works between 5 Celsius and 7 Celsius. Okay? There are some thermometers that work only in between 5 Celsius and 7. It is perfect in that range. It's perfect. That means sometimes perfect up to eight decimal points. Yeah. But only between five and seven. So having a good range is not a must. Okay? Having a good range is not a must. You can have a smaller range too.
Okay? It's okay to have a smaller range too. Okay? Uh based on the scenario, but generally having a good range is good, right? Okay. Then the next thing next thing a good sensitivity. A good sensitivity. What is a s what is the sensitivity? What is sensitivity?
Sensitivity means uh like huge variation. Huge variation with the temperature. That means when you change the temperature by a certain value, when you change the temperature by a certain value, the property should show a visible variation.
That means assume there's a thermometer.
When you increase the temperature by 1 Celsius, it its level maybe let's assume it's a mercury thermometer that you usually know, right? In a mercury thermometer what happens is mercury level goes up and down with the temperature. Okay, clear. Mercury level goes up and down with the temperature.
Assume that when you change the temperature by 5 Celsius, it only goes here. Clear? Now that 5 Celsius difference is not that visible, right?
Using this thermometer or the thermometric property that 5 Celsius difference is not that visible. So if this is for 5 Celsius for 1 Celsius you won't even see right but there's another thermometer or a thermometric property uh for 5 Celsius it changes like this so for sure you would see a good variation for one Celsius difference too right so this is sensitivity okay sensitivity okay how what is the size of the response I get for a certain temperature difference that is the sensitivity so Having a good sensitivity is good. Okay.
But not a must. Okay. Still we can use this. Okay. Uh so these are the characteristics of what?
Good thermometric properties. These are the must. These are the must and these are the generally okay or good characteristics. Generally okay or good characteristics of thermometric properties. Then the next thing is we put these thermometric properties and create thermometers.
Expansion of mercury is a thermometric property. You put that into the mercury thermometer.
Okay? And electromotive force or current is a thermometric property. You put that and produce electronic thermometers.
Resistance is a property that changes with temperature. You use that and create again electronic thermometers.
Okay. Those digital thermometers we we see nowadays, right? Nowadays the most commonly used one is the digital thermometer. Right? Clear. So these are thermometric properties converted into instruments. Okay. So in that case uh like what are the good properties that we expect from a thermometer. I mean this is not this is just like a theory lesson. Okay. I mean not not no huge calculations or anything like that but need to follow. Okay. So this part you would find you won't find this part difficult. Okay. It's really easy the initial parts. The problem is again in heat lesson. This is a very lengthy lesson. Okay. lesson have that has more theory than the mechanics lesson. Okay, this has more theory than the mechanics lesson but very small time to practice. Okay, very small time to practice or a huge le huge lesson. Okay, huge lesson but very small time to practice that. Okay, cuz we don't have that much of time like in mechanics.
Okay, so you have to revise. Okay, heat not now actually after like one or two week weeks we are moving forward with the proper content then what you must do is you have to revise and come to the class for sure okay clear otherwise you won't be able to catch up things okay so what are the good properties of a thermometer good properties of a thermometer uh easy to use okay definitely it should be easy to use should give direct readings what are direct readings there are Some thermometers you sometimes they are very accurate. Okay. There are some thermometers.
You put the thermometer to the location where you need to measure the temperature. Then you see a amter reading, a volmeter reading. You look at the amter reading and volter reading.
Get those two values. Do a calculation.
Calculate the resistance and using the change of resistance you calculate the temperature. Okay. Sometimes there are thermometers like that. Sometimes these thermometers will be accurate up to like 15 decimal points but not easy to use.
Right? So we prefer a thermometer that is it is easy to use and give direct readings. You don't have this issue with the electronic thermometer or the mercury thermometer. Right? You just read the value that's all. Okay? And again having a good range having a good sensitivity. These are the things we expect from a a good thermometer. Clear?
Ah. So the next topic, next topic you have to write this down on book. Okay. A small a small amount of content you have to write. What actually happened was uh I was initially planning to plan in the t such that you are going to write a bunch of stuff. Okay.
uh but uh like on the way I figured out that if it is if you are doing that it is too much so for the first two weeks it was planned in a way that now you had to write some stuff but after the second week you don't have to write anything because everything was is now in the book okay so that's what happened a small planning issue actually okay we were trying I I was initially planning to create a note such that you would have to write a lot of stuff so that you would remember. Okay. Then after one or two weeks of content, after preparing one or two weeks of content, I figure that out. You can anyways remember, go home and study and remember. It's not my job. Uh so let's put everything into the t no need of writing because we have a limited time, right? We are getting a 2our time slot. It is a limited time. If you try to write notes, okay, if you try to write notes, I mean like one and a half hour of our 2 hours would be taken by that. Okay, then it is going to be entirely useless. Okay, so as a result, the first like five pages or first like three four pages are designed in a way that you have to write a certain amount.
After that you have four books like this. Okay, you have four books like this for eight. 1 2 3 4 uh everything after the first three four pages are in the book. So we only have to do the questions and listen. Okay, that's all.
You don't have to write anything from day two actually. Okay, so it was a small planning error. Okay, but at the same time if you write you would remember. So go home and write. Okay.
So let's move forward. Pay attention.
uh like Kelvin scale let's learn later uh like first I mean pay attention pay attention when it comes to measuring temperature one thing is we used to measure we use a certain property to measure temperature but at the same time we need a certain unit right we need units to measure temperature, right?
So, units were created the same way that thermometric properties are handled.
Okay? That means if in a in a when it comes to a thermometric property, what we usually do is we get that thermometric property, we get that thermometric property. Maybe the length of mercury or something, volume of mercury or something, we put that thermometric property two two exactly known values.
Maybe the melting point of water, a temperature that we know for sure and we can recreate it again and again, right? And we put the same set of mercury and we get that value or pressure or something like that. Okay?
You put this into ice water mixture which means it's at the melting point. You get the value of that thermometric property. Maybe the length, maybe the volume, something.
Then maybe you put it into boiling water.
Another good point that we exactly know, right? Boiling water. That means the boiling point of water. Then you get the thermometric property at that point.
Then using this, you create a scale.
Clear? When you create a scale using this now you can tell okay when the thermometric properties value is this this is the temperature when the thermometric properties value is this this is the temperature right like that we can later use the thermometric property to assume everything okay so that is the target we created temperature scales the same way okay so write down the topic temperature scales and the first topic is Celsius temperature scales first topic is Celsius. So write these few like one or two pages and like just staple that to your main book. Okay, it's only for today. You have to write something.
After that your textbook would be required only to do questions.
Okay.
Okay. Celsius scale. Celsius scale. So under that right this so today's stuff is not actually asked a lot in A levels. Okay. It's just there because without learning this we can't move forward otherwise things that we do today you would never see in a heat past paper anywhere okay so today's content is just there for that we have a certain idea about certain things that we are going to use in the future that means when we use the unit Celsius in the future we have to know what is that right like that but these stuff were already there in your Oliver's book okay so we use two steady points. Okay. To create a temperature scale, we use two steady points. Okay. That means we get the again the Celsius scale was created using the two very popular steady points. What are they?
Boiling point and the melting point.
Okay. So, we call this pay attention.
Pay attention.
So we call this the melting point. We call the melting point as zero Celsius. Clear? We get the boiling point and call 100 Celsius.
Okay. Clear? So I it's not that the water started melting at 0 Celsius. So water started boiling at 100 Celsius. We call the boiling point as 100 and the wing point as zero. Okay. So next next otherwise I mean how can they like have that kind of very precise values like how why why isn't it at one isn't that at 1.5 why can't the water boil at 100.03 03. Why it's exactly 100? Cuz we we made that. Okay. So, uh boiling point is 100. So, write this. Write me point here, boiling point here, and write this. And we divided it into 100 units.
This is the this is how we created the Celsius scale. Just common sense. Okay?
So, you don't need very good notes about this. Just common sense. Okay? Write melting point here.
Pay attention. Stop talking.
Write me point here, boiling point here and write zero here, 100 here and put something like this. And you can write this is the Celsius value. This is the Celsius value. This is how the Celsius scale was created.
Okay. Then Fahrenheit scale. Quickly pay attention. Fahrenheit scale.
Fahrenheit scale.
So the Fahrenheit scale under Fahrenheit scale write this again. Write melting point here, boiling point here.
In Fahrenheit scale was created such that they called the melting point 32 fah.
They called the boiling point 212 fah.
Clear? 212 fah. And they create the Fahrenheit scale. Okay. They create the Fahrenheit scale and they divide this divided this into 180 units.
They divided this into 180 units. Okay, that is the Fahrenheit scale. Okay, that is the Fahrenheit scale.
Fahrenheit scale.
Okay, pay attention. I mean pay attention. Uh since we learned these two, we learn we we'll learn about the Kelvin scale too. Okay, pay attention.
Let's learn about the Kelvin scale too.
But this is not the proper time to learn about the Kelvin scale. Later we are going to learn about uh in the heat lesson after like uh 5 6 weeks we have to learn about uh like the state changes okay state changes and using a very specific state they created this Kelvin scale okay called the triple point I think you had that in I can't remember in chemistry yes right in chemistry you have that the triple point kind of stuff. Okay. So, we'll do we'll learn the pay attention pay attention we'll learn the proper Kelvin scale definition after doing the state changes but for now just for the sake of doing the future questions I'll teach about the Kelvin scale not the proper definition but a rough definition about on how to get values that's all.
So uh when it comes to uh the Kelvin scale, why did we need a prop another scale when we had Celsius and Fahrenheit?
Because this Celsius and Fahrenheit both refers to two end points. Okay, two end points and uh like the zero of Celsius didn't mean anything. Zero of Fahrenheit didn't mean anything. This is not a absolute scale.
That means in our SI unit system we always prefer to have absolute scales.
What are absolute scales? If the length is 0 m that means there is no length.
If the mass is 0 kilog that means there's no mass.
If someone all of a sudden come and define that this kind of a length is 0 m then it's really difficult to work with that.
Right? If someone define that okay this is 0 m now work with this it's not very convenient to work with and it is not very accepted in SI unit system and we know from the first day of the lesson the proper SI unit of temperature is Kelvin cuz it's absolute that means like that 0 m makes sense that means the length is zero 0 kilogram makes sense that means the mass is zero But 0 Celsius and 0 Fahrenheit means nothing. We need something to represent the absolute values. That's why we define Kelvin. So Kelvin 0 means the lowest temperature possible in the world. That means I said that temperature means particles oscillating.
This oscillation stops entirely at a certain temperature. Okay. When you keep reducing the temperature, these oscillations of particles they decreases and at a certain temperature this oscillation holds entirely. Okay, this oscillation holds entirely. It stops all the particle stops. Even the air particles moving around us, they moves down and settles on the ground.
Okay, everything settles. That is the lowest possible temperature in the world. We gave that we call that the zero kelvin and we have never been able to reach this temperature. Okay, clear.
We haven't been able to reach this temperature. This is a absolute value where all the motion stops. Okay, all the motion stops and all the particles get what? Particles usually have a gap because of these oscillations. Okay. All the oscillation all the oscillating particles would have a gap because of this oscillations, right? So when this reached to zero, everything would shrink. Okay. Clear? So I mean this is a very ideal situation where you would see this in a black hole or somewhere like that. Okay. Clear? Uh so we have never been able to reach this with the technologies but we have yeah reaching very close temperatures to this value but not zero kelvin. Okay. So we created the like um scale a new scale where 0 kelvin means exactly zero. Okay. Exactly zero. But we made sure that gap between a Celsius unit and a kelvin unit is same. Clear?
That means a gap of 1 Celsius and gap of 1 kelvin is same. Clear? Cuz the scale that we used to use. So gap of 1 kel and gap of 1 Celsius is same. Okay. If someone mentions you that we increase the temperature by 1 Celsius or if we increase the temperature by 1 kelvin it is same. Okay. The gap is same. Okay.
And 0 kelvin is equal to what? 0 kelvin is equal to - 270 3.15 Celsius. Did you have this 15 in knowles?
Oh yes, some have some. Okay. Okay.
It's 200us 273.15 C. Okay. Clear? Ah. So but gap of 1 kelvin gap of 1 kelvin is equal to gap of 1 celsius. Okay, gap of 1 kel is equal to gap of 1 Celsius.
Clear? That means uh like from this you should understand uh so 0 kelvin means - 273.15 and gap is same. That means if you get a certain Celsius temperature, if you get a certain Celsius temperature and add 273.15 to that, you would get the temperature in Kelvin. Okay. Why? See Celsius minus 273.15 you add 273.15 you get zero. That means the Kelvin value. So anyway they have a linear relationship. Why? As I mentioned a gap of 1 Celsius is equal to the gap of 1 Kelvin. That means uh the scales go like this. Scales go like this. This is 0 Kelvin.
This is this is the Kelvin curve. This is 0 Kelvin.
This is Celsius.
Minus 273.15.
Okay. But they grow together. Okay. They grow together. Clear? Their gap is always the same. Okay. Their gap is always the same. Clear? So as a result, I mean uh as a result this is the Kelvin curve.
This is the Celsius curve. Okay. So see this is what is this?
This is 0 Celsius. So this is -273.15 Celsius. This is 0 Kelvin. This is 0 Celsius. Exactly above that you have 273.15 Kelvin. Clear? Clear. Then you would have somewhere like this.
You would have somewhere like this you would have uh 100 Celsius. Somewhere like this you would have 100 Celsius. Then exactly above that point you have what?
0 + 273.15 you get 273.15 100 + 273.15 you get 3735.
Clear. You get 373.15.
Clear? Uhhuh. So you get something like this. Clear? Okay. So their gap is always same. They are linearly increasing together. Okay. Ah. So write this down. Kelvin scale. Kelvin scale.
Write the topic Kelvin scale for now.
This is a rough definition. And we'll we are going to just for the sake of calculations and numbers okay just for the sake of calculations and numbers later we'll work with the proper definition and the main thing is in our syllabus pay attention main thing is in our syllabus we are not going to usually use this 0.15 okay in many scenarios you would see we just add 273 okay we add 273 we are not going to think about this.15 Okay, clear. And this is nothing new. Okay, this you had entirely in all levels. Okay, clear. This cannot be anything new. So, write the Kelvin scale and write the topic under Kelvin scale.
Uh right zero kelvin means absolute zero where all thermodynamic where all thermal motion stops.
Okay.
topic the Kelvin scale under that write 0 kelvin is the 0 kelvin is the absolute zero where all where all thermal motion stops 0 kelvin is the absolute zero where all thermal motion stops. Okay, that's why we needed the Kelvin scale. Now write this down. What is 0 Kelvin? What is the meaning of a 1 Kelvin gap? How to get Celsius? How to convert Celsius into Kelvin and Kelvin into Celsius? And this okay write this down.
Okay.
Uh who created this case? Kelvin. I know it is Kelvin. Others I have no idea.
Okay.
Next topic.
Next topic. Connecting a thermometric property with a scale. Connecting a thermometric property with a scale.
Connecting a thermometric property with a scale. Don't what do you have to write notes only today? Okay. You are not good at writing notes and I'm not good at giving notes. So this this is not going to work out. So from next day onwards you have everything printed on the book.
Okay.
Okay. Pay attention.
Connecting a thermometric property with a scale.
Connecting a thermometric property with a scale.
Okay.
So now this is the story. Pay attention everyone. Pay attention.
Pay attention.
Okay. Connecting a thermometric property with a scale. That means uh now assume you have a certain property. So again what you do is again what you do is you get uh you reach I mean you can definitely find the melting point again and again right all you have to do is find what ice together then you know that is melting point pay attention stop talking there okay and you know now you know that it is 0 Okay, now you know that it is 0 Celsius.
Okay, now you know that it is 0 Celsius. Okay, then you get the property value at that point.
You measure the property value at that point. If it is mercury, it may be the length of mercury. If it is the current, the current flowing at that time or something. Okay, you get the property value. Okay.
Then you reach another point that you properly know somewhere like 100 Celsius. You put that thermometric thermometer or the thermometric material into 100 Celsius. Then you measure the value there 100. Okay. Now we assume linearity.
Okay. If it is not linear, we need computerized methods or much complex mathematical calculations. But if we assume linearity now given the given the property value at any temperature, we can predict the temperature. Right? Why? If it is linear, if it is linear, okay, now I know that when the temperature is zero, the property value is P when the temperature is 100 Celsius, the property value is P 100. Okay, property value is P 100.
And it is linear. We know this for sure.
Okay, it is linear and we know this for sure now. Okay, if it is linear. Okay.
So now assume at a certain temperature at a certain unknown temperature okay at a certain unknown temperature I measure this property as P d theta okay as P d theta then I need to predict the temperature using that what can I to use the gradient right use the gradient that means the gradient is going to be same for all the points so you use the nonpoints P 100 minus P 0 P 100 - P 0 over 100 - 0 clear P 100 - P 0 / 100 - 0 equals something like this. Same gradient. P theta minus P 0 P theta - P 0 / the minus 0 / the minus 0. Clear? P theta minus P 0 / theta minus 0. Now if you know P theta, you can find theta using what?
Since you know every other value, you multiply this here 100.
Since you know every other value, it's not mandatory to use uh the boiling point and melting point. Okay? Based on the scenario, use whatever you can.
Okay? But you have to know two points.
Okay? You need two known points. Okay?
Using those two nonpoints, if you know the value of the scale there, you can measure the thermometric property at that point. Right? Clear? You can measure the thermometric property at that point. That means if it is a mercury, you measure the length of the mercury at 0 C. You measure the length of the mercury at 100 Celsius. Then you assume a linear behavior.
Now you use that property at a unknown temperature you get a random value P theta that random value using that random value you predict the temperature got the idea clear this is the mechanism okay this is the mechanism clear but when it comes to questions uh we usually don't have to draw this okay we usually don't have to draw this we put this rough sketch and using this we write this okay why I mean even here this is the y-axis this is the x-axis right okay so just drawing this would this and writing this would be enough okay clear you definitely don't have to draw this and go here just for the sake of writing now right but when doing questions just draw a rough sketch here okay you don't have to draw a lines graph this is the y side this is the x side this minus this sequence this minus this That's all.
Okay. Uh you can do questions like that.
Okay. So, uh do that and go to exercise one. Write this down. Write this down. Okay. Write this down as an example. You won't see these kind of questions a lot in exams, but you have to have this idea. That's why I'm doing this part at the beginning. Exercise one question.
Let's do a few questions. Exercise one.
Question one.
Question two.
Freezing point equals melting point.
Okay.
Question three.
Question four.
Try these four and 10.
Clear? Pay attention for a second. Even when do when doing these questions to create all the relationships required, use this mechanism. Okay.
Use this mechanism. Clear? That means assume, pay attention. Assume you need to connect Fahrenheit with Celsius.
Fahrenheit with Celsius. You know that 0 means 32 FA.
You know that 100 Celsius means 212 FA.
Now if the temperature in Fahrenheit is this, what is that temperature in Celsius? See, like that you can use this mechanism to connect everything. Okay?
cuz everyone is using the same stable points right here clear everyone's using the same steady points right got the idea okay so to connect everything just use this mechanism okay a proper with a value or two scales or a scale with something anything okay try the questions I'll give like 5 to 10 minutes to try the questions then I'll What?
quickly try to finish the questions online. If you have any questions, mention if you're done with these two questions, finish the exercise. Okay? If you're done with these questions, finish the exercise. Try to finish the whole exercise.
Okay. So, exercise one, you actually don't have to do all the parts of exercise one. I mean, you do one, two questions, you understand the method, then it's okay.
Um, exercise one, question one. Pay attention. Exercise one, question one. The corresponding values of 0 and 100 Celsius. Pay attention. 0 and 100 Celsius.
0 and 100 Celsius uh are + 2 and + 22.
Value shown in the thermometer is when it is + 7 what are the temperatures? So when it is + 7 what is the temperature this divided by this equals this divided by this right?
Clear? Okay that means the same gradient right? So 7 - 2 / theta - 0 = 22 - 2 22 - 2 / 100 - 0. Okay. 7 - 2 / the - 0 = 22 - 2 / 100 - 0. That's all.
Then uh I mean like so you you just solve this and get theta. Okay, you solve this and get theta. Okay, and the next one 12 same thing. Okay, 100 uh 100 means + 2 and + 22. Pay attention.
Uh then when it is 12 when it is 12 what is theta? Okay when it is 12 what is theta? So again this - this over this - this 12 - 2 / the - 0 equ= this - this 22 - 2 / this - this 100 - 0 22 - 2 / 22 - 2 / 100 - 0 Clear 12 - 2 / the - 0 = 22 - 2 100 - 0 clear okay just get the gradient okay and even for like something like minus 8 even for something like minus 8 I mean ideally minus 8 falls here okay ideally uh t 0 means + 2 100 means uh + 22 ideally minus 8 is here you can even write minus 8 here Okay, it's I mean anyways you are going to get the correct relationship. Okay, you don't have to write like this. Okay, it's good if you can write like this or yes, just write it like this. Okay, you don't care. Okay, we don't care until we get the correct answer. Okay, clear.
Okay, so you can even write it like this. Why? any y difference related x difference any y difference divided by related x difference is equal to any y difference related by divided by the related x difference right so you don't have to write minus 8 here okay it's not a requirement just do the same thing okay just do the same thing difference in y over difference of x that means - 8 - 2 - 8 - 2 / the - 0 = + 22 - 2 + 22 - 2 = 100 - 0. Okay, clear. Clear. Are using anyways you are using the same equation. Okay, clear. Is the relationship between gradients? Okay.
Got the idea?
Uh no, there's a question. Can we remember that mathematical equation and use that? Don't you do that. Just you use this notation and quickly do that.
It's easier than remembering that mathematical notation. Okay, clear. Just quickly write it and solve this. Okay, then you know like your uh present in the proper thing whether that you have a proper idea about what is happening.
Oh, there's a weekly revision. Put that in the group. That's a weekly revision for today also like for the class. We'll put that in the group.
Even in essay paper, this is enough.
Okay. Write this. Draw this. You don't have to draw a graph. Okay? You don't have to draw a graph. Write this and get the relationship. That's enough. Okay?
So, when you write this, they know that you know the proper scenario what is happening. you know that there's a graph. This is x values. These are the y values. They know okay next uh there's a small slightly important part in part B that is what is the value corresponding to 80 celsius that also not necessary.
So the other way also you can do. Okay.
That means uh 0 means + 2, 100 means + 32.
Then uh what is 80 celsius? What is the value at 80 Celsius? What is the property value at 80? Okay. So do the same thing. This over this P - 2 / 80 - 0.
P - 2 / 80 - 0 = 32 - 2 32 - 2 / 100 - 0. Okay, clear.
This minus this over this minus this equals this minus this over this minus this. Express your idea about the accuracy of the answers obtained in fifth and sixth parts above.
Okay, I have mentioned that answer there. Okay, because I mean it's not necessarily about heat. Okay, it's not something related to the heat lesson.
What is the problem with fifth and sixth one? Pay attention. Pay attention. Stop talking.
What is the problem with fifth and sixth part? In the fifth I mean we have tested the system.
Two end points of the system are 0 and 100 and + 2 + 22. Okay.
But in the fifth one they are talking about + 30.
They are talking about + 30.
In the sixth one they are talking about minus8. So what is the problem with -8 and + 30? Pay attention. What is the problem with -8 and + 30? What is the problem with minus 8 and + 30? I mean we have discussed this before like I mean we do the test between these two points and sometimes we check the linearity in this region.
So the whole experiment or the scale is arranged in this area.
So if you do did the test in this region, you can't predict out of that.
It may or may not be accurate. Right?
Can you remember? We learned this in uh practicals and graphs part. Can you learn that? Can you remember that? That means I mean we we we tested in this region. Okay. 0 to 100 Celsius.
We tested plus we got +2 and + 22. Okay.
So if we do the p do the practical or did the test until here then it's okay.
But the problem is we have no idea whether on what happens after this point. Right? Clear? We have no clarity about what is happening after this point or before this point. Right? So if you try to predict something after this point or before this point it may or may not be accurate. Clear? Got the idea?
Clear? If we do a certain practical or a test in a certain region, we can't use that practical or the values to assume values out of that region only in that region. Okay. Write that answer.
Okay, the next one. So just write that answer. Okay, just write that answer.
Now you can write it in whatever the way you like. Okay.
Okay.
Next one.
Okay, question two.
Question two.
Pay attention. Stop talking everyone.
Pay attention.
Okay.
A faulty thermometer reads a faulty thermometer reads 1 Celsius for the freezing point. That means there's a thermometer. Usually freezing point is 0 but it reads 1 Celsius. Okay. So this is the reading. This is the actual temperature. This is the reading. This is the actual temperature and it reads 105 for the boiling point. That means boiling point is meant to be 100. The thermometer read is 105.
If the measurement is 52, that means we read 52. Pay attention. Stop talking.
We read 52. Okay, we read 52.
Then what is the correct temperature at 52? Okay, we read 52. And what is the correct temperature at 52? Okay, if the measurement is 52, what is the correct corresponding temperature? So again, this minus this over this minus this, the same thing. Okay, 52 - 1 / theta - 0 equ= 105 - 1 over 100 - 0 cuz everything is just a linear relationship, right? So you do the same for everything. Okay. You do the same for everything. Clear? Okay.
This is like two scales or two properties. Clear? Okay. Some kind of a connection between two things, right?
Some kind of a linear connection between two things. Got the idea? Okay. That means when you draw this, they know that you're talking about a graph actually.
Clear? Okay.
What is the temperature shown in the thermometer for a temperature of 60?
That means this is zero.
This is 100.
Uh, 0 is 1, 100 is 105.
Then uh if the actual temperature is 60, pay attention what is the temperature read by the thermometer.
If the actual temperature is 60, this is the actual side. Okay, they are telling that at 0 Celsius we read one. So this is the wrong side that means the thermometer side. This is the actual temperature side. At freezing point means actually 0 Celsius. It is read as one.
Boiling point means actually 100 Celsius. It is read as 105.
Then if the actual temperature is 60, what should be the reading by that 40 thermometer? Clear? Okay. So this over this equals uh this over this p -1 this is the first part this is the second part over 60 - 0 = 105 -1 over 100 - 0 p - 1 / 60 - 0 = 105 - 1 / 100 - 0.
Clear? You solve this, you get the reading. Clear?
Got the idea? Okay.
On a day where the room temperature is 30, what is the temperature shown by the thermometer?
So on a day like we know that 0 Celsius is read by the thermometer as one. Actual 100 Celsius boiling point is read by the thermo as 105.
On the day where the room temperature is 30, that means the true temperature is 30. True temperature is 30. What is shown in the thermometer? Clear? So again this - this over this 3 - 1 / 30 - 0 = this - 1 5 - 1 / 100 - 0. Clear? Okay, just assuming a linear relationship. Got the idea? Clear? Just assuming a linear relationship everywhere. Okay, the concept we are using is that the gradient is every equal everywhere. Okay, so y difference of x difference equals y difference of x difference everywhere. Y difference of x difference means gradient, right? Clear?
Uhhuh. This is actually the y-axis and the x-axis of a graph.
Obtain a relationship between Celsius and Fahrenheit temperature scales.
Pay attention.
They ask the Celsius scale and the Fahrenheit scale. Pay attention. Stop talking.
They ask the temperature. They ask the Celsius scale and the Fahrenheit scale.
Okay. So now uh what are the things we know?
0 Celsius means 32 fah.
100 Celsius means 212 fah.
Then what is what is if the temperature is written in Celsius as theta C what would be the value of that same temperature using the Fahrenheit scale.
So the same thing this minus this over this minus this. So this is actually a Celsius and Fahrenheit graph. That's all. This is actually a Celsius and Fahrenheit graph. Got the idea? So the same method as before. This minus this over this equals this - this 100 - 0 over this minus this 212 - 32. Okay.
So here we get uh theta c you bring it here 180 over 100 equals theta f minus 32.
So we can get theta fah equ= when you solve this 1.8 8 TA Celsius plus 32 32 So this you can directly use when required. Okay, this is the relationship between Celsius and Fahrenheit. Okay, given the cell temperature in Celsius at a certain point, what is the connected Fahrenheit value? Okay, what is the connected Fahrenheit value? Okay. So, you can use this to convert between Celsius and Fahrenheit. Okay.
Next Okay, next four value shown in the Fahrenheit and Celsius scale. Take the same value for one temperature. What is that temperature? So let's use this directly.
Now we have a relationship between Celsius and Fahrenheit. Now, right? So ta fah equ= 1.8 ta c + 32 + 32 value shown in Fahrenheit and Celsius scale takes the same value for one temperature.
So at a certain temperature you the value you read by the Fahrenheit scale and the value you read by the Celsius scale is same.
Okay. What is that? You solve this you would get the answer. Okay. Clear? Uh so it would be - 32 here.8 theta you take it here. So8 theta becomes -32 theta = -32 /.8 8 this is that temperature where Celsius scale and Fahrenheit scale read the same value okay clear this is that temperature where the Celsius scale and the Fahrenheit scale both read the same value it is -40 that means -40 C is equal to -40 fah okay a specific point where both have the same reading.
Okay.
Is it 18?
Which one?
Uh, yes. Our two nonpoints can vary from question to question but ideally these two nonpoints are in 99% of the questions are 0 Celsius and 100 Celsius.
Okay. The melting point and the boiling point.
Okay.
Next one.
Question 10.
Question 10.
Pay attention.
When the bulb of a constant volume thermometer at 0 C.
At 0 Celsius.
Yeah. So there's a thermometer. Pay attention. Stop talking. Pay attention.
So at 0 Celsius this some kind of this thermometer shows a pressure of 720.
Pay attention a pressure of 720.
Okay. Then at 100 Celsius it shows 1040.
At what temperature does the bulb show the pressure of 1,000?
If the pressure is 1,000, what is that temperature?
So this minus this over this 1,000 - 720 / the - 0 equ= this 40 - 720 over 100 - 0.
Solve this you get the theta value.
Okay, you get the theta value.
8 87.5 theta is 87.5 Celsius.
Okay.
So, uh pay attention. Let's use this and quickly uh go through a few types of thermometers. Okay. Would take like five minutes. Pay attention. Okay.
Finish writing this quickly.
Finish writing this.
So I'll give you a small guideline.
Pay attention. I'll give you a small guideline and go through that guideline and uh read about these three thermometers next week and come to the class. Okay? Read about these next three types of thermometers and come to the class. Gas alcohol thermometer, thermo couple and uh glass alcohol thermal and glass mercury thermometer. So in all these thermometers what we do is for an example pay attention glass mercury or glass alcohol thermometer what we do is we fill a glass why mercury or alcohol then there's a tube a marked tube connected with that then what happens is based on the temperature felt by this Mercury or alcohol, it expands, right?
It expands through the glass tube. Okay, pay attention.
It expands through the glass tube. So based on that, we can read the value. So ideally, pay attention. Stop talking everyone.
Okay. So ideally um like if you like get this from the market, it's ideally scale is written. Okay.
scale is usually written but otherwise what we do is the same thing but you get one stable steady point put it into 0 C and mark the value as L not put it into boiling water that means 100 C mark it as LTA theta pay attention stop talking mark it as LTA theta clear so Uh then prepare a linear scale. Prepare a linear scale and write down the values. Okay, got the idea. Prepare a linear scale and write down the values.
Okay, so for alcohol thermometer also the same scenario. Okay, we prepare a scale. We know when we can find zero, where we can find 100. Based on that, we divide this and write down the values.
Okay, based on that we divide this and write down the values. here and there are good and bad things about all the thermometers like uh take for for mercury thermometer it is a conductor so quickly absorb heat so quickly respond directly direct use you can directly read the value uh and it has a very high boiling point so I mean after the boiling point you can't use mercury thermometer right why I mean the after the boiling point of mercury you can't use the mercury thermometer right why then it starts turning into vapor, right? And below the melting point of mercury, you can't use this as a thermometer, right? Then it turns into solid. So when it comes to mercury, it has a very high boiling point. So you can use this to measure very high temperatures. But it doesn't have a very low melting point. So we can't use this to measure very low temperatures.
But when it comes to the alcohol thermometer, same scenario.
It has a low boiling point but a very It has a low boiling point. So you can't use that to measure very high temperature values but a very low melting point. So you can use alcohol thermometer to measure very low temperatures.
And usually alcohol expands faster than mercury. So when it comes to sensitivity, alcohol thermometer is better. Clear? When it comes to sensitivity, alcohol thermometer performs better. uh and even it is cost effective than mercury thermometer.
Clear? Like that there are different different properties in different different thermometers. Got the idea?
Then another type of thermometer is thermmoelect electric couple.
Thermmoelectric couple means if you choose the proper two types of metals.
Okay. If we choose the two types of metals properly, if we choose proper two types of metals, it has to be a specific combination based on the temperature difference between these two sides and electromotive force will be generated and a current will flow. Okay? And electromotive force will be generated and a current will flow.
And based on this current we can predict the value. And what is good about a thermometer like this is it has a very high range and a very high accuracy.
And the next thing is these thermometers with a bulb. You can't use that to measure the temperature of a surface.
Right? Whatever you measure the bulb should be covered by that. So you can't find a pressure the temperature at a point like this. Right? See then the whole surrounding is air table is only touching here right but when it comes to a thermmoelect electric it's just a contact it's just a contact so that is a good thing about this thermometer but what is bad is in some thermometers it is solved you should do a calculation based on the galvvinometer or the amter reading but the thing is many thermmoelectric couples comes with a digital scale so it usually shows the value. So that part is also removed. So this can be considered as a very good thermometer. Okay. But when it comes to a thermoelect electrical another problem is the electromotive force generated it goes like this. Okay. Electromotive force generated with temperature it goes like this. So what is the problem? Not one to one. So in scenarios like this what we do is we put a maximum That means we tell that this thermometer can be used to measure temperature values only up to this point and we make it 1 one to one. Clear? We give a limit to the thermometer. Okay. You can't exceed this temperature. Anything after this temperature cannot be measured by this thermmoelectric couple. That is the rule. Clear? And even this is a very high value. So no big issue there like thousand Celsius or something like that.
Okay.
So you can see sometimes there are functions that are not one to one functions that are one to many but you can convert it into one to one by giving a leave it to the thermometer.
Clear? You just tell okay we measure temperature only up to this point. We measure temperature only in this region.
Clear? Uh so like that there are some good stuff about thermometers and bad stuff. And again if we take about a thermister not mainly in the syllabus.
Thermo thermister is a electric mechanism to measure the temperature.
Ther is a small device where its resistance changes where its resistance changes with temperature.
So it can be made really small and the temperature can be electrically measured. So you can find like thousands of theisters in your computer motherboard sometimes at least five six why you know that your computer motherboard check the temperature at different different different points right it do a self test always so you can't have these type of thermometers there right clear that thermometer whatever you are using should be really accurate but should be really small there we use theers and it can be electrically measured Okay. Why can it be electrically measured? Because it is the it is the resistance, right? Since it is the resistance, you can electrically measure using the resistance. You send a current pulse, check the voltage, use V= IR, get the resistance, do a small calculation inside the motherboard and get the temperature. Okay. Uh so there are different types of uh temperature uh like thermometers.
What I need you to do is um like read through this part and finish exercise two and come cuz next week we are starting the main topic in heat lesson that is uh main topic in heat lesson that is expansion. From there only we start doing real questions. Okay, this is just a part an introductory part where we learn about measuring temperature. Okay, that's how we start the lesson. Next day only we are starting the real heat question part that we would see in the past papers. Okay.
So finish until exercise two and come next week.
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