Black body radiation follows Stefan's Law, which states that the total energy radiated per unit area per second is proportional to the fourth power of the absolute temperature (I = σT⁴), where σ is the Stefan-Boltzmann constant. The emissivity (ε) of any real object ranges from 0 to 1, representing the ratio of energy emitted compared to an ideal black body. Wien's Displacement Law states that the wavelength of maximum intensity (λ_max) is inversely proportional to temperature (λ_max × T = b, where b ≈ 2.9 × 10⁻³ m·K), meaning as temperature increases, the peak wavelength shifts toward shorter wavelengths.
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Sanjeewa Dharmawardhana | Rapid Revision | Physics | English Medium
Added:Good morning everyone.
Especially for 2026 Alevel batch people students. We are ready to launch the very first ever English medium advanced level program with other than education.
So let's start this and we have a small plan and starting from this week till you go to the exams in August 10th we are planning to send you lot of interesting topics what you have missed. You know that these days we were having a big chat because you are a group of students who face little bit of unfairness because of the time constraint they had. So what we thought very thoughtful idea with other than an education every morning from the national television plus in the YouTube channel. So you can see you can watch and you can learn very last few lessons in your syllabus in case you covered it at the last moment with a very rapid revision program with all the past paper discussion.
Let me tell you unit number nine 10 and 11. So we'll start from 11 and we go back to 10 and 9. Unit 11 is matter and radiation. The only quantum physics theory is there in advanced level. So we do that one and section wise 11.1 to 11.6 and we do one by one and then we do the past paper questions to revise the entire syllabus entire past paper history of the past paper sections from the starting date to the last year. So then we go to unit number 10 and unit number nine mainly 9 10 11 targeting for 2026 advanced level students who are sitting for the exams.
Okay. So very good luck. We'll start from 11.1 11.1 black body radiation black body radiation.
And we are going to discuss the past paper but we have a special idea special program concept inventory. So what does this concept inventory means? Completely the points what you supposed to learn supposed to learn for the exam. It's not 100% theory. It is mainly targeting the questions coming in the exam. So let's go with the concept inventory. So black body radiation Stefan's law, black body radiation winds displacement law, plank's hypothesis.
So we are planning today these first three concepts. Black body radiation Stefan's law black body radiation winds displacement law and black body radiation black body radiation planks hypothesis.
So we'll go to the Stefan's law first as a revision. So let's quickly go through this topic. Stefan's law as a statement you can say the total energy radiated total energy radiated per second in a unit area from a unit area is in other words is the intensity of the radiation proportional to the fourth power of fourth power of the thermodynamic temperature that is what we call as keelvin temperature. So the stfan constant is a universal constant and that is sigma is the constant of proportionality we call it as stfan's boltsman constant. So the value will be given in exam you don't have to focus on the numbers you don't have to focus on the numbers uh we discuss here.
So these numbers will be given so you don't have to study those parts. E no now there's a small cons consideration because E E is not energy this is the radiant intensity intensity of the radiation so uh there is a reason for E as well actually it is epsylon uh in you know the early stage of the subject when they develop the subject but when it come to syllabus so we have used it as E so surface area of black body unit surface area of black body T is the thermodynamic temperature or you can say the Kelvin temperature.
So coefficient of surface emisivity. Why are we talking about a coefficient of surface emisivity? It's very simple. We are planning to uh match this black body radiation to the real world examples.
Now you know that the black bodies the ideal sort of black bodies are the sun emitive type of black body. Black holes are absorption type of black bodies. So how do you match this to the real world examples? Do we have real world black bodies? No, not not really. So we only have uh approximate black body types. So then we match this to the any kind of body. That's why I like that the word anybody right that's why I like the word anybody so the ratio between the amount of heat emitted by any object any object compared to the black body energy emitted by a surface energy emitted by a surface energy emitted by a surface of a black body with the same surface area, same temperature during the same time frame. So same duration, same surface area, ideal situation compared with what the real world example. So this value is always in between zero and one. So if it is completely a black body, you understand the emisivity will be one and if it is not emitting at all, so that is considered as zero. So you know that emissioning emission is zero means it's 100% absorbed. So absorption type of a black body it is a zero value. So you can say a black hole. So this is kind of the sun right solar system solar radiation right. So yes so we go to the next one that is coefficient of absorption. So we are talking about the absorption type of black body like black hole. So real world even when we go out under the sunlight very warm conditions our skin absorb the radiation. So that radiation is explained by the absorption coefficients. So the energy absorbed by a surface energy absorbed by a surface the total energy fall onto the surface.
In this case, we don't want to compare the black body because the total energy fall onto the surface if it is absorbing 100% we can say it is one. If it is not absorbing at all, we can say it is zero.
So the emission type of a black body it is zero. So absorption kind of a black hole type of a black body it will be one.
So the summary so this is very important frame you to remember simple terms if you in case don't understand oh I can't remember every single word I explained in the previous slides so take this one this is your short not to do numerical questions let's take this one black bodies black bodies I have kept in black color so I BB BB very easy to remember BB black body sigma T ^ 4 this is the intensity of a black body sigma T ^ 4 power P is powers because I am trying to take intensity in terms of power so power of a black body BB PB is sigma into area because power is energy over time so I can say intensity I replace by power and the energy of black body ebb sigma a t to the power 4 into time. So we remember these three formula will help you to do all the questions associated with the black body. So the other side there is a little bit of colorful part what is this I usually call black body anybody anybody not one word two words any object. So intensity of any body I A very easy to remember IB I A B E emissivity or you can replace absorbs coefficient of absorption sigma T to the power 4. If you want the intensity of a black body sigma T to the power 4. If you want intensity of anybody E sigma T to the power 4. If you need power of a black body sigma a T to the power 4. If you need power of any body simple E absorption coefficient or emissivity sigma a into t ^ 4. If you need energy of a black body sigma a t ^ 4. If you need it for anybody you just multiply this black body component by the emisivity or absorption coefficient.
So that is the simple summary of the whole lesson and we can do lot of questions. Before that we go to the next concept called wind displacement law. Most of the time the black body radiation connected with the intensity distribution and winds displacement low. So let's go for a big diagram.
Right? So this is the intensity variation. Now you need to remember several features of this. So you look at the corner first. So this corner you can see there is no intensity intensity no intensity at the very small wavelength because this is the radiation spectrum of all electromagnetic waves. So we'll take the smaller curve first. Smaller curve first. So this is at 4 4,000 Kelvin at 4,000 Kelvin. So 4,000 Kelvin this is how the intensity variation with the wavelength. So the very large wavelength you have lesser intensity very small length you may not have intensity at all but the medium wavelength you can see the intensity become large. So here it is 4,000. So you increase the temperature of the body to 5,000. So when you increase it to 5,000, you get this you know the hype of the intensity. So the largest hype is recorded for the maximum intensity.
Maximum intensity increase the most. The other intensities also you can see increased. So here increase of the other intensities and the largest increase for the largest intensity. So you bring this 5,000 into 6,000 you can see that 4,000 to 5,000 temperature change is the same but intensity variation will be really high. So 6,000. So this is more closer to the variation the surface of the sun.
So when you reduce it, it drastically reduce. Now we'll put this into words.
We put this into words. Now you know the diagram diagrammatic explanation. Some people have the picture memory. People who have the picture memory remember this. Or else what you can do? You can remember this in terms of sentences. So how do you remember this in terms of sentences? The couple of lines. The intensity is very low at large wavelength and very small wavelength.
intensity is low at the large wavelength as well as small wavelength. So it's kind of a bell curve you know that so maths people they know that the normal distribution curve we talk about normal distribution curve. So always the middle part is more and the extremes are less.
So that diagram is also here but I keep it in a small scale because I'm more focusing on the sentences. All intensity values corresponding to each wavelength increases with the temperature. Always when you increase the temperature all intensity values increase but the largest variation of intensity will be recorded for the largest intensity.
Largest variation of intensity will be recorded for the largest intensity. The wavelength associated with the maximum intensity is shifted to the low wavelength region with the increase of temperature. You can see that the wavelength associated with the largest intensity is coming towards the left. So it goes to the left. So my point is this. So I'm very keen to explain this value. You can see these values these values these values are coming from right to left start from here coming towards this coming towards this. So this is what we call as this is what we call as the winds displacement low. So now after you go through these three special lines you can develop the winds displacement low.
Now we said this idea very clearly.
So maximum wavelength associated with the intensity distribution inversely proportional to T because when you are increasing [clears throat] the temperature when you are increasing the temperature wavelength will be decreased. So you can do the cross multiplication and you can bring this formula very easily. You can remember lambda max that is the maximum wavelength associated with the intensity maximum variation maximum wavelength associated with the intensity into time into temperature thermodynamic temperature is equal to C that is the winds displacement constant. So means displacement constant value you can see that the value so you can see that the value so 2.9 10 ^ 3 2.9 into 10 ^ minus 3 so this is me kelvin so that is the wind displacement constant and that is a that is a very unique constant that is a very unique constant right So now we try out some past papers from this. We try out some past papers from this and see whether you can grasp this idea. Can can these past papers be very complicated and difficult? No, they are very straightforward and very easy. Unit number 11 is something you can easily score. So even at the last moment you study this, you go through this and you can try this. I request if you are watching a recording from your YouTube channel. So what you supposed to do post the video here do the question always and then meanwhile what you can do you can go through the answers and test yourself whether you are ready for that. So one question question number one little bit older version of it right which of the following statement regarding thermal radiation is not correct. So that was actually not the foot that 11.1 time 1995 very all syllabus but the conceptually it is perfectly matching with no harm. So thermal radiation is electromagnetic in nature. Yes or no radiation is electromagnetic in nature. Right? And object which is good absorber of radiation is also a good radiator. It absorb it emits. It absorb emit. So when it absorb whatever it is absorbing can be emitted. Radiation loss in thermos flask are reduced by silvering the walls of the glass. Yes. Because silvering surfaces are less em dark color sometimes. Always remember it is nothing to do with the surface conditions in the reality of the black body radiation but in the nature of the real world. Real world examples are slightly different. So we go to fourth one. Heat cannot be transferred from one place to another through radiation only.
[snorts] It can the best example is the sun. So you get the heat from the sun purely through the radiation. So they are expecting incorrect statement. Incorrect statement is what? The fourth one. White clothes are recommended for hot sunny places.
Yes. Because white clothes are good emitters. So it emissions good emitters. So it emits well. But on the other hand, on the other hand they are not very good absorbers. So when we are not absorbing lot so it will feel little bit comfortable when you are wearing. So before we go to the new syllabus 1997 change of the syllabus the next question I think we'll revise the idea. So figure shows the variation of the intensity of radiation I emitted by a black body with the wavelength lambda.
As the temperature as the temperature of the black body increases the maximum intensity I am increases and the position IM shift towards longer wavelength utter. So it is very simple answer. IM increases And the position of im shift towards the shorter wavelength. Yes, that is what we learned. When the temperature increase, it will go like this. The position shift to the left. So that is what we have learned.
So I like to tell you this idea very easily.
Let me explain and rei revise this part before we go to a short break. So what we are learning here is 11.1 that is that last topic with other education very first ever English medium program. So we are planning to start from unit number 11. We are planning to start from unit number 11 and coming back to unit 9 and 10. After a short break, we'll discuss the other past paper questions.
[music] Right, just after a short commercial break. So, we are going back to the black body radiation. Black body radiation is always about this. The sun radiates energy. Now this is 1999 A level question. The sun radiates energy at the rate of E per unit surface area. Radiated energy at E. Rate means rate means rate always mean what? Per second. So rate per unit area. What does it mean? Energy divide by time divide by area. So that is what we call as intensity. So intensity we know the theory part very easily right you people understand. So black body I have given you a very simple formula to remember this formula is I BB IB sigma T to the power 4. So for the black body so we can go with sigma t ^ 4 divide by that and get the root value.
So the final answer will be the first one and this is absolutely theory. So 1999 they have given a perfect theory lesson part you to remember. Now tell me can I tell you something? Sometimes students do this small mistake when they try to attempt past papers. They select the random past papers or sometimes they select um 2025 the most recent past paper. I'll give you a small hint because these exams are slowly evolved.
So when they're evolving they always try to do something in a nice pattern. They try to teach you the lesson. When we discuss these things with the professors who are in universities who are getting involved with the marking or paper settings or teaching physics subject in the universities they usually tell you this because sometimes they don't get the chance to teach you all straight away.
They don't get the chance to teach you all straight away. So what do they do?
They can teach you a small lesson at at once to the entire country. How? Putting a question to the exam. So that exam the batch who are writing the exam not only them from all the future generations they can go through the question and understand the concept or you can teachers can teach this part. Now if you go through the question previous question they asked a simple theory of the intensity distribution variation of intensity distribution with wavelength.
In this case they gave you the Stefans Bolsman law. So then they can next year they can go for the next step stage or next level of the question. So what I try to tell you so always when you're trying to do questions my request if you're selecting a lesson start from most of the time start from the year they introduce this topic. So they introduced this topic meta and radiation in 1997 1997 A levels. So from that point onward they were slowly evolving the lesson to this level. So you can see when you're going through the work with me now. So we go to the next question figure shows.
Now you can see the same question.
Earlier they gave only one sentence. Now what do they do? They are giving three sentences to check whether you understood the previous year. Now this is 2002. Earlier it was 1997 or 1998. So they give this lambda figure shows the black body radiation curve for a body at a given temperature. Given temperature no change of temperature. There's no change of temperature. So they are talking about lambda m as well. Okay, let's go to the sentences. Lambda m would be lower. Consider the following statement at higher temperature. So we all know that now we draw the higher temperature curve. Higher temperature curve.
I think it's my my diagram is little bit too closer. So let me redraw it for the higher temperature curve.
So redraw it for the higher temperature curve. So yes, it is shifting to the left. So lambda m would be lower. Yes, intensity would be higher. Yes, it is intensity increase. Lambda decrease.
Yes, velocity of the emitted radiation would be higher. We have no idea. Now this is also another important lesson for you. This is also another important lesson for you. Let me tell you this.
Now they're talking about velocity.
Did I teach that part in the lesson or the summary I was giving you? No, I did not. Why? There is no connection to velocity. Sometimes when you go to the exams, your teachers had taught these lessons nicely and you study them and the examiner give you a weird wrong answer. When the examiner give you weird wrong answer, you people get confused.
Oh my god, our teachers did not teach this. So you start blaming either teacher. So remember this sometimes we can't give all the wrong answers in our notes because wrong answers are wrong.
So we give the correct answers. You trust your gut feeling. You trust yourself. Most important is trust the process. You trust the process. You go through the process. You learn the lesson. You do all the past papers.
There may be some weird lessons, weird answers which we have never ever given or heard. So what does it mean?
I'll keep it for 5 seconds. Think what does it mean?
The answer is wrong. That's why it's not learned. That's why it's not taught. So always remember if you come across something, believe your gut feeling, believe your science, believe your instinctives. just mark it as wrong if you have never ever heard before under that topic. Right? So let's go for this one.
Black body temperature TK TK means T Kelvin capital T kel sorry capital T kel radiates energy at a rate of 10 mwatt at temperature 2T. Now they're comparing.
Now when they're comparing, so what do we do? We develop a theory for the comparison. So I like to explain you the idea. Since Stefan's Bolsman constant is a universal constant, we can say that IBB intensity of radiation of black body right T^ 4 proportional to T ^ 4 because this is a constant. So we go to this.
Now in it is proportional we can develop this interesting format. So this is a very popular format in A levels. This is very popular format in A levels. So two quantities are proportional. What does it mean? Their proportions are equal. I always like to tell this to my student proportional.
Proportional easy to remember.
Proportions are equal.
Proportions are equal. Proportions are equal. All the ratios are equal. So we take the ratio. We take the ratio.
Right?
And now the second case it is 2 T. First case it is T. So 2 to the^ 4. And we know that it is 2 into 2 into 2 into 2 that is 16 and you get like 160 mwatt.
That is fifth answer. That is the fifth answer. So this is easy. Now can you remember this is 2006 question earlier 2002 they gave you the formula after couple of years they asked the first stage work what is it to compare the two black bodies with the same conditions right so you always start from the beginning and slowly develop yourself to 2025 so keep doing the past papers focus on them and start from the initial stage page of the lesson and let yourself develop with the evolvement of the questions.
So a star s okay um I'll take that one at last I think that is better because there is a pattern of questions I like to take the pattern first if the absolute temperature of a body is doubled ah now 2007 now previously it is 2006 they ask the same kind of question right same thing you can see the same thing not difference at all so Even I add the same calculation without any hesitation. I added the same calculation without any hesitation. Why? Because earlier they gave a value. Now they are giving the fraction or the ratio only.
So it is again 16 times. That's why I skip the previous one. So you can see that it is 16 times increase 16 times.
So 2008 the temperature of a sunspot and and they talked about this sun sunspot and umrah uh in Alevel essay paper as well. If we have time before your exams we'll do the essay questions as well. So the temperature of a sunspot is 4,000 kel and now they're asking a fraction again while the surrounding solar surface is 6,000. So the intensity of the sunspot and surrounding solar surface. So what do we do? We use the same pattern but the only difference is now here they have given a different digits 4,000 the real value approximately a real value 6,000 approximately a real value. So it's matter of simplifying. So you can cancel this you know the th00and here and 4 is 2 into two. So you can cancel the two factor and then you will get again 16 into 16 over 81 as the answer. So you can see the pattern they slowly develop.
They gave the theory in 1998 2001 2002 and then 2006 they gave the real comparative model question. 2007 they repeated 2008 they came to a real world example with approximately real value. So it's a nice development of the process. You also have to follow the process and trust the process.
So the total energy radiated by a black body is collected for a minute and used for heat a certain amount of water. Now, now they come to the next level theory comparison comparison little bit realistic comparison further and then comparison in the real world.
Example, now they connect this radiant energy to other topic of the syllabus, other topics of the syllabus. Now they can easily connect the radiation with heat, right? So they try to use this heat radiation to heat water. So now we have to take heat lesson little bit.
Unfortunately we are not ready to do the entire revision of the heat lesson. But we can easily use the equation and start this over. So now we come up to this point.
Why I say this number?
Now you can see that in 2011 they gave the same number because they double the temperature when the temperature is doubled now you did it three four times what happened the heat will be 16 times right so we are using it to the next work Q equ= M ms delta theta so sometimes some people use C I use S because S is a nice letter and it it is my my name also start from S. No, not not because of that. Not because of that but because S I like to use it for specific heat capacity. I keep C for heat capacity. Specific heat capacity S heat capacity C. So I like it that way.
Right? So it doesn't matter when it comes to MCQs what symbols you use. Even the essays you use like the more uh you know more more sensible letters can be uh taken into the consideration. So same amount of water and you can see that the temperature difference I write it for another scenario. So in the first scenario the temperature of water increases from from 20 to 20.5 if the abs absolute temperature of the black body was doubled. So what happen is that the heat emission radiation or the rate will be four 16 times and temperature of water would increase from 202 they start from the same temperature as well. So let's go to the next slide.
So now you can see the new case it is 16 times than the previous case and MSMS because we are talking about the same amount of water initially it is increased from 20 to 20.5 now it is 20 to ta so we are going to find what is ta and it's a matter of simplification and 28 celsius and answer will be first one answer will be first one I think this is a quite rapid revision. I know that because you are very closer to exam. I don't want you to go through anything slow speed up your work. But in case you want, you can post these videos and watch them slowly again from the YouTube channel. And kind advice, don't put it at 1.5 speed. Why?
Because I'm anyway going at 1.5 speed.
So you take your time and go through it.
Whenever you stuck get stuck, you stop this, pause this and go through the note and go to the lesson.
Okay. So, let's go for the next one.
Again, just a small uh clarification at the middle. Which of the following is not true regarding the rate at which a body emits radiant energy? Now, they go for little bit of you know a sentence wise idea. So, we'll take our note into the discussion. Which of the following is not true regarding rate at which a body be careful it is not a black body. A body emits radiant energy. It is proportional to surface area of the body. What do you think? Is it proportional rate at which? So we can go with this one. Is it proportional to area? Yes, it is here. Right.
It is proportional to fourth power of the absolute temperature.
Okay. What do you think? Is it proportional to absolute fourth power of the absolute temperature? Yes, it is. It is proportional to the emisivity of the surface of the body. Yes, it is because you can see that emisivity there.
And then it does not depend on the thermal capacity of the body. Now couple of minutes back I said this. Have we learned anything related to thermal capacity of the body? No. Then why are they like trying to confuse you with that? I told you when they want five answers. So you have P A 1 2 3 four only four they are in the right hand side one they are in the left hand side and one of them that is Stefan's constant is a universal constant so you can't talk about a variation with a universal constant because it's a constant so they lack of they are they ran out of answers [snorts] wrong answers so they they pick some random stuff like what capacity heat capacity of the body so that is useless So don't ever think about it does not okay. So we know that we have to ignore them. If we have not learned don't try to think overink no it's object is like this and it it may be like depending on the object properties or the material don't don't don't don't just stick to the formula when you're learning physics MCQs not learning physics completely when you are trying to attempt physics MCQs best thing is write the formula write it correctly and go through it and finish this off right now then the obvious wrong answer is the fourth one.
It depends on the temperature of the surrounding. Okay, now this is a little bit tricky. Before we finish the day, we have to talk about it. There is another formula and examiner will ask it next slide. Let me give you a brief idea about it before we go to that. This is 2012 AL question.
So yes, it is wrong. I will sh talk about it and I want you to remember this particular slide. So let me underline it using red color regarding the rate at which the body emits. Oh the rate at which the body emits.
Okay. Rate at which the body emits. Keep it in your mind before we go to the next part. So let me take the other question and explain. The rate at which a body emits radiation depends only on the body's own temperature, surface area and MCBT. It does not depend on the temperature of the surrounding. The temperature of the surroundings affects the net rate of heat loss. Net rate of heat loss. And keep that line in your mind and put a special note on this because the next question will be from that. And one more thing examiner imply you the certain things I told you at the very beginning examiner's intention of doing past papers is not just evaluating you sometimes he try to they try to the panel tries to do something they try to teach you lessons and then you get the depends on the temperature of the surrounding so you have to be very careful why he is talking about the surrounding so the teachers dub also you know trigger that and teach that part very quickly not after the uh lesson is question next year. This is 2012 and you should understand when you refer last couple of years of the questions what is coming this year is very obvious sometimes it is slightly above what you have learned up to this point.
So let me take that one a little bit because because the surrounding also emit radiation towards the body. So that can be given we call this part the effective radiation.
So in simple terms when we radiate say I am the body which radiates when I radiate when I radiate the surrounding also radiating towards me external temperature controlling the net change.
So here net change is what I provide to them and they provide to me. So we get the difference to understand the effectiveness of this. So let's sorry so I keep it for some time quickly note down this this will be the last conceptual part we are doing today. So okay so this is the difference I was talking about that's the effective value. This is the surface temperature sorry surrounding temperature. Sorry about that. This is the surrounding temperature.
This is the surface temperature of the body. Right? Okay. Can you see in 2017 they gave you the idea about the surrounding and 2017 after five years they question it. Be careful with that.
So when you are studying past papers is they are not just questions. Sometimes they are clearly showing you the path for the next question.
A person with surface body temperature 30 is an environment of temperature 20 the net. Ah now what is the difference between this one and the previous one?
Earlier it was the rate. Now this is the net. So when they talk about the net energy right when they talk about the net energy we have to get the difference of course. Now you know that effective idea we have learned it in the previous question. Now this is what they expect us to know right. So now I like you doing the balance questions we have brought it up to 2017 17 to 2025. There are another four five questions and with the time constraints we may be not we may not be able to discuss all these questions but we try to tell you this and give you the um support for your lessons. Let me let me give you another opportunity. Now if you are watching this from the television go to Adarana education YouTube channel and the Adarana education YouTube channel this will be uploaded and then what you can you do you drop the comment in the comment section. So in the next video next day we are definitely answering your questions and please remember to drop a text and drop a uh comment or question to the Adena YouTube channel.
So this is the very first ever lesson other than an education has done as the English medium lesson for English medium students and this will be a continuous program. This is not only just one day work and we see you with the 11.2 and we are finishing entire 11 10 and 9 before your exams. Stay with us. See you next day early morning at 5:30.
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