 Let us say let us reach steady state, now we are in radiation there should not be any time required to reach steady state. So getting back so I said this is the Planck's distribution so this was the Planck's distribution if I plot this I am going to get let me repeat this at the cost of being repetitive this is y axis is emissive power spectral emissive power and x axis is wavelength and each legend is each legend is temperature. So this is what I want to tell another thing I keep telling this in the class also somehow I miss that any graph I show in the class should first be told what is x axis this is what I have learnt from my teacher what is x axis what is y axis what is the legend that is the that is first thing we should tell that is what I have done now. So if you see here what we see here is there are no contributions other than ultraviolet visible light and infrared towards thermal radiation. So then there is I do not want to spend too much time there is only one point I want to harp on is there is the peaks if I join the that line can be represented by lambda maximum t equal to a constant and which happens to be 2897.8 micrometer Kelvin and this is what is called as what is this called Wien's displacement log. So I think with that we will move on to this is professor Wien again so he has also got Nobel prize I said radiation is full of Nobel prizes so he has also got Nobel prize for his work is I think so it is getting displacing towards the as the temperature is increasing the peak or the location or the wavelength at which my temperature sorry the emissive power is maximum is getting displaced that perhaps I do not know I have not read anywhere specifically written that yes I guess what is the physical significance of means displacement law see perhaps the I think with this law he could predict the sun's temperature he could predict the sun's temperature this all happened independently you know Planck did this work independently Wien independently did this Wien perhaps did not get the distribution but he got independently lambda max into t equal to that constant this was all independent observation I would think why we attribute so much significance for Wien's displacement law is that professor Arun can add on to this is that he independent everyone at that time was trying to predict the sun's temperature and they knew the wavelength range for the sun's emissions so around that wavelength range they could predict they knew everyone knew it was around 5000 plus temperatures of course there were uncertainties in the temperature measurements they had different methods I do not know myself exactly how they measured the temperatures and how they had that data but they had the temperature data of the sun and every theory whichever theory was proposed was checked only with one check that was the sun's temperature why because high temperature data was simply not available to check their theory so that was the minimum thing the what they could check so to answer your question why we attribute so much significance to Wien's displacement law is after you have Planck's distribution it appears pretty trivial but what if someone has found it independently that is what it gives so much significance that is what it gives so much significance that is what he was one of them were asking he was Hemant was suggesting that is it because the peak is getting displaced with the increase of the temperature that is our guess only I am not too sure about that no no lambda max T the peak is getting displaced with the increase of the temperature that I can see from that relation itself now I do not have to see the Planck's distribution for that. Yeah let us see when did they get the noble price this guy got in 1911 and Planck got in 1918 that is true that answers it but Planck gave from in fact Professor Bandarkar derives this when I say professor Bandarkar from advanced thermodynamics class Akhet should remember this or Sandeep if he has attended he comes from fundamental Boltzmann statistics and derives this Planck's distribution one can derive this he derived from the theory of from the theory of quantum theory photons each my electromagnetic wave instead of wave theory he adopted quantum theory wherein which my energy is being transmitted in the form of packets that was adapted and he could come up with this relation okay so that is why both of them got noble prices yeah so to answer your question so it tells that that is the best part of putting the historical perspective that is Veen's displacement law was found much ahead of Planck's distribution that is why it carries so much significance so much significance okay now if I integrate this for the old wavelength I am supposed to get back my sigma t to the power of okay so but then historically it did not come this way sigma t to the power of k m first sigma was figured out by Boltzmann later on from Boltzmann statistics and then everyone was convinced about 5.67 into 10 to the power of minus 8 okay so now I think with this we can move on to what is band emission that is to make our calculations easy in today's world I do not know whether this band emission concept is important or not because I can just apply Simpson's one third rule because if someone is interested in fraction of the emissive power between a wavelength 0 to lambda as opposed to 0 to infinity that fraction this fraction in today's world I can numerically integrate in my calculator itself so I do not have to really use these tables but I think these tables were generated when computers and calculators were not there and logarithmic tables were used so what they have done is they have derived sorry they have defined fraction 0, lambda what does this f 0, lambda represent fraction of the total emission from a black body that is in a certain wavelength interval that is all it is so if I this is e lambda , b d lambda this is sigma t to the power of 4 so I do mathematics I just take lambda t equal to m d lambda t equal to dm d lambda will become dm by dt my limits also will get changed so f of 0, lambda will be will become 0, lambda 0 lambda t to blah blah blah I then put e lambda , b pi i lambda , b this is Planck's distribution where in which I have put pi inside so f 0, 0 to lambda can be seen as a all the circus I am seeing I am doing essentially to see inside the integral as functions of lambda t that is all I am trying to do so once I do I get that as a function of lambda t once I get that function of lambda t so it is just a representation this is the emissive power of a black body varying with a wavelength this is the fraction I am trying to represent this shaded portion divided by fully area under the curve is what is I am talking about as f 0 to lambda so this if I put that again coming back f of if it has to be that was for 0 to lambda, lambda if it is between lambda 1 to lambda 2 I can write this as 0 to lambda 2 minus 0 to lambda 1 so that is this figure explains or tells us how to visualize this so now I lambda , b this is just to put the in tabular form I lambda , b is emissive power upon pi so this equation upon pi again if I see this is again brought in the form of as a function of lambda t now I can compute at any temperature I can compute and that is for a given lambda t these are computed this integrals are computed and kept so that is for a given lambda t I have fraction between 0 to lambda t and I have I lambda , b lambda t upon sigma t to the power of this is put in the tabular form I think you can all see this and this is very nicely put in one problem if you solve this problem you will be able to appreciate how to use that table I know I have gone rocket speed but there is no concept involved here so that is the reason why I have consciously gone fast but in main workshop we will have to solve this problem all the problems in the main workshop while teaching itself will be solved in tutorials the problems will be different that is just to make sure that but please ensure that everyone will have calculators will have calculators and hopefully the notes material with them let us see how do we go about that yes we will try to upload it a week before so that you can have the complete information they can have a printout as I said with one side for notes making okay so but you have to monitor them you have to be with the what you say militarily you will have to monitor them okay okay so fine surface emission now ideal thing is over now we have to get to real surfaces because no surface I do not say no surface is a black body I over coffee there was a discussion going on how do we get black surface I did share this information but I guess I need to tell this for everyone so typically I said the black body is generally created by I get I create an emissivity of one by having a cavity but other way is we try to make a perfect emitter perfect emitter is my making by painting played by putting black paint typical black paint what we use our matte finish we use these paints why I am saying this because I want to give one suggestion in your experiments that is why matte finish any paint earlier Asian paint used to come nowadays that paint is not coming matte finish black any supplier paint black paint okay and it is good to paint not with the brush but with play painting so that it gets uniformly distributed otherwise very very traditional is lamp black that is you put your plate over the candle candle is again a diffusion flame lot of suit will be generated so if you put the plate over that candle reasonably thick candle with a thick wick you will be able to generate more suit but you will have to ensure that you uniformly run over the plate so that you get reasonably good black and of course blackboard paint but we have to be little careful when we are using blackboard paint because nowadays many blackboard paints are having that glaze so that the reflectivity is there so what I was trying to say is that we I see in all of your setups most of your setups you have very similar setup like what we have that is you have a real surface in a blackboard so you get the emissivity one way nowadays in India we are able to get thermal guns thermal gun so which will give the directly the emissivity I will try to get sake get that thermal gun today evening we will just show that I will show you the thermal camera and the thermal gun what we use for measurement of emissivities so you can go ahead and use that if that is giving the emissivity you can vary the temperature and get the emissivity as a function of temperature number one number two you can cross check your emissivity measurements whatever you have done with the other method so that way you would have introduced them to thermal camera thermal camera as I was saying one of you asked what is a thermal camera we use thermal camera thermal camera also will be brought in the afternoon I will show you what is a thermal camera thermal camera is nothing but a small resistance small resistance but then there are multiple resistors let us come to multiple resistors little later there is a small resistance so when thermal radiation occurs that is when it is when it some energy is incident on it so what happens mine resistance increases that resistance increase is a measure of heat flux it only measures the heat flux it does not measure anything else it only measures the heat flux so if you know the emissivity only you can get the temperature it is again heat flux is what professor has been telling heat flux in radiation is emissive power so that is equal to sigma t to the power of 4 so sigma epsilon t to the power of 4 if I know epsilon the measured emissive power whatever it is in terms of voltages actually it will be but in built there are some nowadays programs it will do the calculation and give us if provided if I give the emissivity if I give the emissivity okay so we need but now in a thermal camera the beauty is that now we duplicate that that type of resistance plenty are there how many it can be typically how many how many number 240 by 240 by 360 if my memory goes well so many pixels are there you use pixels knowing the camera technology use pixel 10 megapixels you use that similarly in thermal camera you have that many thermal resistors and each thermal resistor imagine each thermal resistor should not talk with the another thermal resistor that is where the micro machining comes into picture that is where micro machining comes into picture so many 320 by 240 pixels are embedded so if you take a plate of this size so you can resolve it in 320 by 240 pixels so each pixel depends the size depends on your size if you are measuring this plate you can as well go up to as much as 1 mm or even less than that okay the point is you try to purchase the thermal gun if someone is having a money to the tune of 2 lakhs that is enough to purchase a thermal camera in today's world if you want any information on that I would be happy to share that information and it is a good idea to have thermal camera in each of our institutions it gives you surface temperature that is all it is required wherever you why do you use thermocouple for your convection we use in convection we use for convective measurement we use temperature measurement if I maintain a plate at a constant heat flux boundary condition how by voltage and current and if I measure temperatures I will get my heat transfer coefficient so radiation can be applied to measure heat transfer coefficient okay so I mean what I am trying to say is thermal camera alone makes us understand emissivity much more otherwise emissivity is a very abstract thing that is the reason why I am saying at least we understood emissivity reasonably well only when we started measuring things with thermal camera okay so anyway at the end maybe if we get time I will share some information about emissivity measurements in fire and all what we do but that will be the faggest end not anywhere here okay so I do not want to bore anymore fine coming back so what is that we are doing is so emissivity is emissivity is radiation emitted by a real surface upon radiation emitted by a black body at the same temperature what is kept same temperature okay so this is the spectral variation so emissive power of a black body is this means real life thing is going to be spectral variation it is going to be there and also it is going to have it is going to have what does this right hand side figure suggest directionally dependent okay so there are various definitions I am going to go not very fast but I am not going to derive them I write them because professor Arun has spent already ample time on this so I do not want to harp anymore on this because he has told what is spectral what is directional so spectral directional emissivity means emissivity is a function of wavelength direction theta gamma phi and naturally it has to be function of temperature earlier we had we had fixed the temperature now temperature also I have embedded for a given temperature emissivity is equal to intensity of radiation emitted by real surface to that of black body for black body I am not writing theta gamma phi why because it is diffused it is independent so this I guess we can understand I lambda comma E lambda comma theta okay next what is total directional emissivity what does total mean it is been averaged for all wavelength so it has to have only directional dependence so epsilon theta subscript we use only theta to suggest that it is having directional dependence theta is theta comma phi comma t equal to I E theta comma phi comma t upon I bt lambda I have thrown because there is no wavelength I have integrated over complete wavelength next is what is next can anyone explain atul patil will you please explain me what is spectral hemispherical emissivity spectral means yes but it is it is hemispherical means it is integrated over complete hemisphere so theta comma phi complete theta 0 to pi by 2 1 0 to 2 pi we have integrated so that is why we are writing if there is no directional dependence I do not have to use any longer intensity I can use emissive power that is why I have written E lambda lambda comma t upon E lambda comma b lambda comma t okay so one can relate spectral hemispherical emissivity to directional emissivity so if I take spectral hemispherical emissivity that is E lambda lambda comma t so that is how did I write this equation where did this come from this is the equation spectral hemispherical emissivity is epsilon lambda lambda comma t equal to E lambda lambda t is the integration of all so similarly for black body it is integration of all but only thing is that this I lambda comma b lambda t is independent of direction so I can put that out of the integral but I will put it in the numerator because I can take it wherever I want because I can pull it out of the integral so I put it upstairs this if I integrate I will get something but what is this what is this alone I lambda comma E lambda that is a spectral directional emissivity so that is what is epsilon lambda theta lambda theta phi t if for a minute if I assume that it is independent this is all again hypothetical it need not be that way if it is independent of phi I can take 2 pi outside why because here also I get 2 pi so if I do that algebra I can show that epsilon lambda that is hemispherical emissivity is related to spectral directional emissivity this way this is this is this derivation ensures that we have understood the definitions properly that is all nothing great and of course I can have integrated every way that is wavelength wise and also direction wise total hemispherical emissivity you can write this equation so because there is no direction now so I will have only epsilon lambda this can be derived the same way what we derived here okay if you really want okay so now we can go find rest is now just doing the calculations whatever we have done see if I have to get average emissivity if I have spectral emissivity like this how do I average them out what does this transparency tell now I will start asking questions because we have given all basic principles now I will hand randomly pick anyone and ask questions okay shublam on can you tell me what is that I am doing in this transparency see what is this figure saying it is having an emissivity one near about see I am having red colored spectral distribution I am assuming that it is constant up to 0 to lambda 1 like this and there is again lambda 1 to lambda 2 it is again reasonably constant and then again lambda 2 to lambda it is constant I have broken it into three portions between lambda 1 lambda 2 and lambda it is up to lambda that is to infinity that is that is the range okay so now because question is where do I get this type of things where do I get this type of things emissivity we can get this do not do not think that this is just like that generated actually there are spectrometers I also learned very recently there is something called as FTIR spectrometer FTIR spectrometer it will measure and give me do not ask me how it measures because I do not know so it will give me the emissivity as a function of it can give in fact transmissivity and reflectivity okay in fact it does not give emissivity directly sorry it gives transmissivity and absorptivity transmissivity usually for all rough surfaces for all solid surfaces is 0 it actually gives reflectivity from which we will infer absorptivity and from there we will say that it is emissivity you will understand I will again broach up this issue when we introduce absorptivity transmissivity reflectivity but what I am trying to say is this I want you to emphasize maybe by main workshop I will put a small cap here and say what is FTIR I will I will try to put a cap but what it what I want to emphasize is that this is not out of the world picture in real life one can measure emissivity spectrally varying emissivity okay so that is what I wanted to emphasize it is not just for the sake of cooking we are cooking it is indeed like that so sometimes you want to measure emissivity of diesel sometimes you want to measure emissivity of petrol liquids also I mean we should not imagine all the time it is only solid surface it is possible even for liquids and gases definitely it is possible okay okay so yes someone asked the question is that okay or the question is how can one measure gases no the gases is if it becomes participating only air reasonably it is not participating it is participating with a short wavelength but that can be neglected okay that is how thermal camera works thermal camera is seeing a hot body but in between what is there air is there because air is reasonably non participating thermal camera is able to see the hot body okay so now what am I doing here what am I doing here I have to write emissivity equal to eb lambda upon eb isn't it that is emissive power of the real surface is epsilon into eb lambda right but between 0 to lambda 1 epsilon is epsilon is epsilon 1 constant so that is why I can pull that out of the integral so this is spectral variation and this is averaged over because 0 to infinity in the black body so that is how and this ratio we have already put that as fraction previous so within each wavelength range for lambda t I can get this fraction if I put those fractions I can get for a given temperature I will get lambda 1 t I will see that table I will get that fraction lambda 2 t I will get that fraction here 0 to lambda 2 t f 0 to lambda 2 minus f 0 to lambda 1 and here again lambda 2 minus infinity how will I do this f lambda 2 minus infinity how will I do that 1 minus area under the integral is 1 0 to infinity is 1 f 1 minus of f 0 to lambda 2 if I do that I will get that so that is how I am integrating and getting this emissivity and as I said it is coming out through FTIR sake please note down I may forget I have to add this here FTIR what is an FTIR spectrometer okay Fourier transform infrared spectrometer oh okay I remember how does it work okay how does it work FTIR spectrometer works on Planck's distribution okay good I was unhappy with myself okay so FTIR spectrometer what is Planck's distribution yeah this is my this is my Planck's distribution using this Planck's distribution therefore FTIR my temperature has to be fixed therefore my FTIR my temperature has to be fixed so independently independently it measures the emissive power by a sensor by a sensor and on the right hand side now my temperature is my temperature is constant and now for each lambda for each lambda I can compute the emissive power so it is essentially working on Planck's distribution it is working on Planck's distribution in fact I should be quoting another example what I came to know through Professor Ramakrishnan they use FTIR spectrometers in satellites why because if they put FTIR spectrometer in satellite and take the satellite picture what do that see they see all soils you know all rocks which mineral is there is where they will identify through a concept of emissivity image processing they do image processing because Isra always we see in one of the objectives identify the rocks and various minerals I used to wonder how they will figure it out I learnt through Professor Ramakrishnan. That is I will come to that I will come to that I will come to that for gases here I am in solid actually FTIR for identifying if what professor is trying to say is FTIR is also used for we are digressing but that is okay FTIR is also used for exhaust gas analysis for example IC engines exhaust gas you want to know how much is CO how much is CO2 how much is nitric oxide and all FTIR Fourier for each sample there is a standard signal standard FTIR spectrum which is fixed if you get CO if you say CO they will match with the CO spectrum if they will calibrate the FTIR with CO alone CO2 alone NO alone then you can see each one that is for that is for gases that is for gases but what I am trying to say here is for solid yes for solids also they will generate inbuilt they will generate library but that is coming from the concept of that library is coming from the concept of emissivity emissivity this is how emissivity is useful in various situation okay anyway thanks to professor Ramakrishnan okay. Hello and of course FTIR spectrometer is very expensive it costs near about 75 lakhs okay it is very difficult to have but if you want to do any FTIR spectrometry we have safe scientific analytical instruments facility sophisticated analytical instruments facility if you send the sample they will not charge you more than 1000 rupees or 1500 you can get it FTIR spectrum you can get what I mean is if you are taking a black surface if you are very much in research mode and you want to show your students real spectrum you get that black surface once taken FTIR spectrum that spectrum you save it with you spectrally averaged emissivity you can spectrally average it and get the emissivity with the gun you can get the emissivity another method you get another emissivity so different methods you have shown them how to see the emissivity in all this remember there is no directional dependence I am telling always the normal emissivity is that okay that should be in the back of our minds okay. So see what I am trying to say is when you do experiments only you will learn the concepts better okay so that is the reason why I am giving you so many ways of measuring emissivity so that you can reach your student very fast if you show him FTIR spectrometer rather than giving him this cooked problem and ask him to average it he will understand okay this is how I need to apply it for my real life okay so I think we can help you if you need any help about safe if you go to safe plus IID Bombay in Google you will be landing in safe website yeah I think I can write that SAIF sophisticated analytical instruments facility they have seen it you have seen it but virtually you can send send the sample you do not have to physically come you can send the sample they will send you it is just one spectrum they will scan you and send you that is not at all difficult okay so I think we can all offer 1000-2000 rupees it is not at all difficult it can be done both not only for solids but also for liquids but for gases it becomes involved let us not generate the gases yeah so now with this let us move on with emissivities of course here it is quite difficult to offer explanations although I am going to do hand waving only honestly because I cannot go to refractive index level and explain things okay it is observed that let me tell it is observed that emissivity of nonconductors are generally higher than conductors okay maybe because the refractive index is better in a nonconductor I do not know I do not know let me not offer any plausible explanation but all that I can say is that this dependence of emissivity with a conductor or nonconductor is can be explained through refractive index that is all I think I can offer you okay so because it is quite difficult we will have to go to if you have to go to see let me show you if I have to really show you what I mean see what modest does is what modest does you see this let me remember this page number 101 if you would see let me spend some time here so that at least we can offer to that extent what it is see if any light electromagnetic wave can be thought of as an optical light if any light passes through I will have when it refracts I will have a real component and the imaginary component n and k n and k now what he is trying to show through various models which I am not trying to show is you see here reflectivity here rho is reflectivity let me come down little more then you can see reflectivity this is rho is reflectivity his notation emissivity emissivity and reflectivity for example this reflectivity is a function of refractive index basically this all these properties are going to be functions of refractive that is why now I realize why people have catalogs of refractive indices for various material this is true for liquids also this is true for gases also okay and it so happens that these models work so well it is not that it is simply a model see these are the experimental results and this is the model it is not that it works all the time but reasonably these models are working but the point to carry home is that the emissivities reflectivities transmissivities they are all they are all functions of emissivities reflectivity transmissivity although I have not introduced I am assuming that you know that but we will come to that emissivity reflectivity transmissivity absorptivity they are all dependent on refractive index okay for a suit particle also for a suit particle also they give n and k that is the real path and the imaginary path from that only one estimates the emissivities and reflectivities and transmissivity. What is what is the meaning of refractive index yeah please go ahead when lighting No it does not reflect it only means that it does not refract the incident angle is equal to the refracting angle yeah what now I think it is like this what is happening electromagnetic wave if it is passing through a medium if it is passing through a medium what is happening it has to undergo scattering it has to undergo reflection so this scattering how much it scatters under what angle it scatters is what it is deciding you are getting my point are you with me or not can anyone elaborate what I told maybe instead of myself telling the same thing again and again see I am I am having all let us imagine it is no longer be a straight line yes if it is having a refractive index not equal to 1 if it is equal to 1 it be a loss it indicates how much it is getting it is getting how much it is scattered that is the reason why all these properties are being explained through refractive index I think to our students if we tell this much this much only we can offer I do not think we can because I do not think it is possible it is possible for us to go back we can do that modeling but for advanced heat transfer courses perhaps but not to derive this and show that for this material this is going to be n 1 n 2 it becomes we will be cutting him off from this but I think we can just explain that it is a function of refractive index because electromagnetic wave is moving like a light and how much it gets refracted is an index of how much it is getting scattered how much it is getting reflected how much it is getting this diagram is still I think you can you can show we have not shown this we can you can see how much that bend that bend is the measure of reflection for a light ray we are able to understand or when you put a spoon in water that spoon in water we are able to understand that right it is a bend. So, that bend is a measure of refraction now extend that concept to electromagnetic waves it will not pass through normally meaning normally is not the right one normally it is not without getting deflected or refracted whatever. So, that property by which the electromagnetic wave is changed whatever way you want to call it that will be governed by the nature of the material which is called as a refractive index. I think that that is the only possible explanation thinkable I mean that is the easiest explanation one at an undergraduate level see what will happen if the ray is exactly what it is if the medium is changed and that it is perpendicular to that surface. No it has to get scattered no even if it is it has to get scattered no it has to get scattered. What is scattering what do you understand by scattering? Because if we put this spoon vertically it looks vertical and if you put it inclined it seems to bend it looks vertical but in the height this here. It is a vertical we have studied no virtual height. No how do you explain scattering what is scattering? Otherwise how do you how do you explain usually how do you explain all these intensities? Actually. How do you explain in your classes? This is what we attempt and we try and that is where we stop in our classrooms here. Scattering now this refractive index comes to picture where the medium gets changed. No here also medium is getting changed no because it is coming on to my plate for example if I take a plate it is it is coming on to my plate. Yes that is what we are talking about. Scattering is going on. Scattering is going on. Scattering will occur like if I shoot a view of like a torch. It will scatter in a particular area. Yeah so if it is for solid surface it is quite difficult to explain but I was visualizing that for gases which are embedded with various suit particles for example. If I have a flame in which that is what I was visualizing but of course it becomes difficult for solid body to tell you are right. For solid body scattering cannot perhaps occur. Actually blue is sky in the morning, red is sky in the evening scattering or flight. Scattering or flight. Scattering or flight. Because of heat band and heat band. Scattering. I do not see the light. That is again participating but my air is participating but here I have to tell it for solid body. I think we will stop here because the tools what we have in our at our end are not sufficient to explain everything that much we should. Do we define scattering in solid? We do not use scattering in solid sir. Scattering is only in gases. You are right. You are right. Let me think maybe before. No no no scattering. No you are right. Scattering cannot occur in solid. Solid. It cannot occur in solid. Okay okay I will stop here because I do not think I have any closed form answer for this. So I do not want to I do not want to go overboard and tell we do not know. But definitely we do not know that much I can tell okay. So but it is quite difficult. All that I suggest is that we will say that we can explain it through refractive indices. That is what is being done. That is what we can tell and be done. Otherwise we cannot explain any of these why it is increasing because students are going to ask me why it is increasing, why it is decreasing either with temperature or with wavelength. I cannot explain otherwise okay. All that I am going to take the recourse is that it is dependent on the refractive indices and how the refractive indices vary that is how these are going to be. Of course I am hand waving now here. So refractive indices for this liquid gas is solid for everyone but scattering is only for gases. So here we are talking is about refractive index. That is every equal to all. Yes. So we are talking here about only of refractive index. So here we are saying that all that we said is that all properties are functions of refractive index. So then I think that much only we can offer. This just as we are discussing I thought of this question. If you have plain water if you keep it in a vessel and we shoot light through it beaker for example we will be able to see the light at the other end also. Slowly decrease the temperature of water and it is starting to form ice. It is not formed ice fully. It is starting to form ice in our, it is the same water chemical composition but we start to see less and less of the light at the other end and when it is full ice hardly anything is also visible. Probably ice is a perfect, what is ice? Perfect black body. Perfect black body but it is for light. Visible in the visible region? Yes. To what that example is always quoted in textbooks. Color is not an indicator of black body. Ice can also be a black body that is what is. So color we should not go by the color of the body. Through visible as through naked eye, through naked eye. Okay. I cannot take any more questions on this because I myself do not know. So we are simply hand waving. We are discussing on something what we do not know. So I am just taking, I am just telling, I am just suggesting that we can perhaps explain through refractive indices and I have not done my homework properly. So I do not know. That is the best thing. But definitely without the knowledge of the refractive indices we cannot explain any of these. That is all I can say. Okay. So let me see before our main workshop can I cook some one or two examples to explain this. Okay. Okay. So now with this we will come to. Okay. Now the concept I think I can now go fast because we know that anything which is g means professor has taught us that it is irradiation. Anything which is irradiating can get transmitted, can get absorbed, can get reflected. So if we do the budgeting g equal to g absorbed plus g reflected plus g transmitted. If I divide it by g, this is g abs by g is absorptivity, reflectivity, transmissivity. Some of all this is one. Okay. If you do energy balance budget for this, which term would be e in, which would be e out, which would be e generated? What is e stored? b, n, e, g. E generated. There is no e generated. E stored. E stored will be absorbed. Absorpt. Absorpt. E generated. Great. Fine. So now we have for opaque surface, generally all solid bodies are opaque. So tau is equal to 0, so alpha plus rho equal to 1. Rho is reflectivity and if my surface is reasonably diffused then I can neglect the reflectivity also. So then I can get the absorptivity. But then I am interested in emissivity. So I need some other tool to tell me how to link this absorptivity to emissivity. So before I come to that, whole lot of definitions are there which I defined for emissivity and similar lines you can define absorptivity, reflectivity and transmissivity. I am not going to do that. I am not going to do that because they are in the same lines. So there is no point in doing the same thing. In the word of caution, whatever be the subscripts and the whatever be the subscripts and the terms inside the bracket, the dependence, same should be there in the numerator and denominator. So apples and apples only have. What what professor is saying is if I am using I here, here it has to be I. It cannot be E here and I here. If the top is lambda, bottom also has to be a lambda. That means it has to be a wavelength specific quantity. So another important thing is that absorptivity, absorptivity is dependent on, there is a basic difference between emissivity and absorptivity. What is the basic difference about the temperature dependence on emissivity and absorptivity? Emissivity is dependent on the source temperature. Not the source temperature on the temperature which it is emitting, which is being emitted. But for the absorptivity of a surface is dependent on the source. That is let us say here this is a good example. If you see if there are emissions by building, there are emissions by sun. So here sun is sitting at the temperature 5780, but building is sitting at temperature 300 kilo. For the emissions due to building or from the building, the absorptivity of my surface that is the concrete is again 0.9, but on the other hand for the emissions which are coming from sun, which are at higher temperature, the absorptivity is 0.6. This is here I am not talking about, okay that way wavelength, yes wavelength of the source. When I fix my temperature, wavelength band gets fixed because my thermal radiation band gets fixed. So the point is the absorptivity of the surface depends on the conditions of the source. This is very very important point why because in Kirchhoff's law I am going to say emissivity equal to absorptivity, but people say even in Kirchhoff's law says that is the most abused equation because when I make emissivity equal to absorptivity, as you saw you will be able to measure absorptivity. Now you want to infer emissivity, but we should take care that whatever absorptivity you measured at whatever temperature should be the same, at the same temperature only the emissivity will be equal to absorptivity. If it is a different temperature emissivity and absorptivity are not same. This point has to be emphasized that is the reason why I have put this transparency here. We have to revisit this transparency when we teach Kirchhoff's law. In Kirchhoff's law we are going to do that hypothesis and going to say that emissivity equal to absorptivity and of course we write within the bracket temperature T, because it will not get registered in our mind because we always say okay I got absorptivity by Kirchhoff's law absorptivity equal to emissivity, but it is not so, so we have to be careful. Because in experimentalists also use this usually make this mistake why because we tend to make this mistake because for measurements you measure the absorptivity usually with a spectrometer which is at the room temperature because FTIRs usually do not work at high temperatures you have to do some jugglery to get it at high temperature, but you want to use that emissivity at high temperature because radiation is usually used for higher temperature. So what we tend to assume this absorptivity whatever we have measured equal to the emissivity which is going to be used for higher temperature. So we need to emphasize on our students that this emissivity and absorptivity can be equated only at the same temperature, but the absorptivity is the function of source temperature and the emissivity is the measure of or it depends on the temperature of the surface from which the emission is occurring yes, yeah how can I answer can anyone answer this how can we answer yeah, this is a difficult question to answer yes, but the question is my surface it is coming on to my surface is it not dependent on my surface at all then sorry, but we are saying correct, but then why it should be dependent on the source you are talking of a specific lambda, but if I fix the temperature I get a band range of lambdas which I have to deal with I am not fixing my lambda max I have a range of lambdas at a particular temperature now even I have this question I do not know the answer so why should a concrete roof absorb something from the sun differently than something from a building or why do you say absorptivity is monochromatic no why monochromatic you mean it is a function of wavelength yeah it is function of wavelength then we are on same page yeah. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . you are just taking this example it may not be true suppose the root is considered as 300 Kelvin it amids laid as compared to when it was at 5780 it means that the stored energy will be higher than that of this out of this. See it is fine I do not think we need to answer all questions let us carry back home for the sake of record for the sake of record I am recording this and we will continue this discussion on model I am noting down two questions today in this we have not answered these questions convincingly that is question number one how do I explain the emissivity variation emissivity variation of conductors and non conductors and other variations I would say we can say in general how do I explain emissivity variations again next question I would say emissivity variations with lambda and temperature how can I explain that number one number one and two number three why is absorptivity function of source temperature why it is these three questions we are carrying back home okay and another thing I wanted to tell you is definitely while reading you will get enough questions already I have a mail from professor Gaitan desiting why no questions why no discussion so you have seen that I guess so I we would encourage you argue implore upon you to throw questions at us not that we will be able to answer all questions but we will start discussing on the discussion mode in model before December but before December we should have answers for all these questions and at least that is a forum where in which we can all discuss otherwise who will I ask okay so let us so this is an opportunity to answer these questions we will definitely ask our colleagues we will read we will get back to you but at least we need to we know now know that these questions have to be answered is that yes sir okay okay let him complete okay you are telling again the observation only no you are not telling why it is not answering the question observed it question is you are right you are right question question is why why so why so why so why so we are going to the root of the no it cannot be answered here the maximum amount of energy towards the peak let us see that is not convincing to us but definitely see we need to because we are all teachers we can appreciate our problems we need to appreciate that these are the questions to over period of three months I am sure one of us should be able to come out of this come out with an answer let us see who will come up first okay so the so yeah what is the thermal radiation and solar radiation why solar radiation different from thermal radiation no radiation is in both the places we mean what in both the places what are we trying to utilize what is the radiation we are interested in solar radiation is the term used for the radiation coming from the sun okay okay what is the question okay let me read that I have brought chengal because since yesterday so much of chengal chengal was going on so I have brought that chengal we will see what is that statement and see that okay as I understand solar radiation is the radiation from the sun on to earth that is solar radiation that is the understanding I have it will have its own wavelengths and all of course there is a clouds and all they are not participating so much thankfully that is why we are we are able to get the sunlight okay I am going to stop all questions and I am going to move ahead with only one point that with only one point that human only one point I want to emphasis again human body is made of water so emissivity of water is emissivity of water is 1 okay so I quote this example always in the class predator movie I always quote in the class okay not always any time when I remember I do not know how many of you guys have seen the movie predator so in the movie predator the hero I do not know who is that hero, hero kills that predator only through that because the predator sees the human being as a thermal picture it sees only the color so he will close himself with some leaves or something so that mud sorry so that there is no thermal picture there is no thermal picture basically he makes himself emissivity 0, 0 the point here is my body emissivity is 1 I can measure the body temperature very easily with the thermal camera when I am using thermal camera when that fever was there what was that fever some fever was there no when swine flew when swine flew was there in all airports if you have seen NDTV or CNN IBM you would have seen everyone watching no we were we are watching on the passengers through thermal camera we are matching the temperature we are monitoring or quarantining the people who are having swine flew how did they find out through thermal camera why they could measure through thermal camera because the body emissivity is 1 whoever is having temperature more than the normal temperature 33, 34 whatever they were they were sidelined and brought back to doctor so that we could exploit that without intrusively I mean it is not you do not have to put a thermometer imagine you measuring temperature with thermometer with all guys in the airport it is difficult with the thermal camera you could just measure and figure out who is having who is having flu okay so that is another advantage I quote this example why because we can relate the utility of emissivity easily how beautifully has brought in a movie concept to explain emissivity one of the few people who analyzes movie from no no actually this is when I saw the movie perhaps I didn't know what is a thermal image but off late only I realized that okay that was this okay