 Now we are getting into the radiation. By the way, in your textbook, there is supplementary material also for radiation. If you flip your pages, go to the backside of the book. There are supplementary material for respective chapters. Don't start flipping right now. Okay, let's talk about radiation heat transfer. Now we know that every object is made up of electrons, protons and neutrons. Okay, what happens is that any object, since it is made up of charged particles, and you are going to learn in class 12 that when a charged particle accelerates or there is some vibration, it will emit EM wave. Have you heard of electromagnetic radiation? Okay. So this EM wave, if the wavelength of EM wave, if it lies in infrared zone, then I will say that there is a radiation heat transfer. So basically every matter on this earth emits EM wave. Okay, like we as humans also, we tend to emit the EM waves, all right, because there are charged particles inside us because of which our entire body is made up of. So when they accelerate, when there's some lattice vibration happens inside it, because of that, there is a radiation transfer that happens. Now this vibration and acceleration, you cannot get rid of. The vibration of the electrons and the protons will go away only at absolute zero temperature. That is minus 273 degrees Celsius. So if your temperature is above minus 273 degrees Celsius, the electrons and protons of the substance will vibrate and it is going to emit EM wave. And this EM wave only, we are saying that this is radiation heat transfer only. Okay, but how come if object is emitting radiation, if it is not at absolute zero, how come the temperature of that object remains constant? For example, let's take an example of bed in your room. The bed is continuously emitting radiation. EM wave it is emitting and every EM wave it emits, it's like it is emitting heat. So why the temperature of the bed is not going down? It is emitting a heat, so its temperature should go down, it is releasing heat. Why it is not going down? Anyone? Because of the air present. Because it is not only releasing heat, it is also absorbing heat. Okay, so if rate at which the bed is releasing heat is same as the rate with which it is absorbing the heat, then the temperature of the bed will not change. Okay, so there is an equilibrium that is there. Okay, so this kind of heat transfer was extensively studied by Stephen Boltzmann, by Stephen and Boltzmann, two scientists. So they have come, they have came up with an expression of heat transfer in the case of radiation. So if there is a radiation that is happening, then the amount of radiation will be equal to this. So we will do this. Please write down sigma EA t raise to power 4. Okay, where sigma is Stephen's constant. Okay, its value is 5.67 into 10 raise to power minus 11. We are going to come back to the units of sigma. Let me define everything else. E is the emissivity. It has no dimensions. It is a fraction. It could be between 0 and 1. A is the surface area and T is the temperature of surface. Now tell me what is the unit of Stephen's constant? Anyone, by the way, this is 10 raise to power minus 8. Sorry about that. Okay, what is the unit of dq by dt? dq by dt is joule per second, right? Which is also equal to the power unit which is watts. Okay, joule per second is watts, right? So watt per meter square per Kelvin to the power 4. So this is the unit. watt per meter square per Kelvin to the power 4. Okay, so this is how you do it. And one very important finding. All of you please write down is that radiation is a surface phenomenon. It does not matter what is the temperature inside. It only matters what is the temperature of the surface. Okay, and also it only depends on the surface area. It does not matter what is the volume. Okay, and when I talk about emissivity, emissivity is a measure of how much fraction of heat will be absorbed or emitted relative to a black body. So basically it is assumed that a black body is a perfect emitter or absorbed. What it says is that whatever radiation that falls on a black body, what is a black body and a body which is whose surface is black and how do you determine the black color? Black is basically is not a color. Okay, black is the absence of color. So why a certain object is yellow because all other colors that are falling on that object, they get absorbed but yellow light is reflected back. So you are able to see it as a yellow color. What happens to the black body is that all the light that is falling on it, it absorbs. So nothing actually got reflected off. So it becomes absence of color. Similarly, when it emits the radiation, then also it emits all the kinds of wavelengths possible. So it is assumed that the black body can emit the maximum amount of energy as a radiation. And similarly, a black body can absorb maximum amount of heat energy due to radiation. So what about an object which is not perfectly black? Let's take a brown color or a red color. To take into account of that, we have factored in E. So E could be equal to let us say 0.8 for brown. So you need to substitute here as 0.8. Then you can use the same formula which was meant for the black body for non-black bodies as well. For the black body, E will be equal to 1. And you can directly write sigma A t raised to power 4. So at times in our numericals, it will be written that assume the body is black. So then it means that assume the value of E to be equal to 1. Fine. Okay, let us proceed. Sir, when we are finding radiation of a body with surface, are we taking? Surface area. Yes, sir. It can have more than one surface. Which surface are we considering? Total surface. I am assuming that all surfaces have the same temperature. If all surfaces do not have the same temperature, then every surface will radiate corresponding to its own temperature. Fine. You can divide the surfaces based on their temperature. But if entire surface at the same temperature, you can take entire surface at once. Sir, this rate is not the same as the rate at which the body that absorbs heat. Yes, that is what I am going to next. Okay. Please write down dq by dt, the rate at which the radiation is emitted will be equal to sigma E A temperature of the surface. Don't write T s, temperature of the body, you can say T b, ratio power 4. Okay. And the rate at which the heat is absorbed will be equal to sigma E A temperature of surrounding to the power 4. Fine. So with what rate the body is absorbing heat depends on the temperature of the surrounding. Okay. Now the surrounding temperature you can manipulate. You can take a hot object like this and put it inside a sphere. Then for this object, the temperature over here is a surrounding temperature. Okay. Surrounding temperature doesn't always mean the atmospheric temperature. Okay. So the net heat transfer, please write down the net heat transfer will be a subtraction of this emitted minus absorbed to sigma E A T b raised to power 4 minus T s raised to power 4. Okay. So if T b, temperature of body is not equal to T s, then what will happen? Let's take two cases. If T b is greater than T s, what will happen? Net net, it will release heat and because of the releasing heat, temperature of the body will go down. And if you assume temperature of surrounding will remain same, as in surrounding is big, let's say atmosphere only, then you can't change temperature of surrounding. So only T b will go down if it loses heat and as soon as T b becomes equal to T s, dq by dt will become zero. Okay. And if T s is less than T b, then what will happen? Absorption. It is same thing which I have written. Pay attention. If T s is greater than T b, then it will absorb. Okay. Understood. So if T s is greater, temperature of surrounding is more, then it will absorb the heat. Same thing. All right. Now let us say the mass of the object is M, specific heat is S. Then can I say that dq is equal to M s dt? dt is a change of the temperature of body. I can say that, right? And dq by dt will be equal to this by dt. So I can equate these two to get a differential equation. I hope I'm clear. If a specific heat is S, then dq will be equal to M s dt and dq by dt will be M s dt by dt. Small t in the denominator. Okay.