 We will get started with the lecture today. So, we will just take a quick recap of what we studied in radiation 2 yesterday. We said that there is a black body and the black body what is the nature of the black body? Black body has three characteristics. One is it is a perfect emitter, perfect absorber and it is diffuse. It has no preference for direction. So, and then we said that the emissive power of a black body is given by sigma t to the power of 4 and this is what is called a Stefan Boltzmann law thanks to the efforts of both professor Stefan and professor Boltzmann. So, this is the relation which was given by Boltzmann and I mean derived by Stefan and Boltzmann. Boltzmann, Stefan found this by experiments that is simple empirical correlation, simple curve fitting, but Boltzmann did the derivation of sigma to get a get us 5.678 into 10 to the power of minus 8. Otherwise, that constant was obtained through theory, but the beauty is that the credit goes to Stefan because he chose t to the power of 4 that is the major credit. The power 4 is given by Stefan and 5.678 into 10 to the power of minus 8 theoretical derivation is given by Boltzmann. The very fact that Stefan had the ingenuity to choose t to the power of 4 that is where his contribution comes. The very fact that the heat transfer the delta t it is the temperature difference is not no longer linear in case of radiation he had perceived that through that relation. That is the beauty of empiricism. People make a criticism always that oh no this guy has done experiments and just given the empirical relation only when you make an observation you can start thinking of explaining it. If there is no observation how do you explain it? So the first thing is first step in research is that one has to go and make observations. Something is decreasing something is increasing now we will start thinking how do we explain this increase or decrease that is how the research progresses. So we should not be criticizing people who are making observations and giving us correlations. But if we should we should criticize those people if they do not explain it to us those correlations. So we should try to make an attempt to explain the experimental correlations whatever we are arriving at in whatever research we are doing. So then the cavity can be visualized as a black body black body if the cavity is a perfect absorber and then emitter. And spectral black body emissive power is the amount of the radiation energy emitted by a black body at an absolute temperature T per unit time per unit area per unit wavelength this is what is Planck's distribution. And we have Planck's constant and C naught do not forget this C naught. C naught is the mother of all everything here. The very fact that C naught you see here that itself suggests that my electromagnetic wave is nothing but light that itself suggests that it is light. So it is the velocity of light in vacuum 2.998 into 10 to the power of 8 meters per second. So k equal to 1.3805 into 10 to the power of minus 223 joule per Kelvin universal Boltzmann constant. Now you can see Boltzmann's why it is called as Boltzmann constant. So Max Planck did this and we if we put emissive power for a black body which is pi I b because it is a diffuse emitter. So I get pi I lambda b. So if I substitute that I get new constant C 1 and C 2. C 1 equal to 3.742 into 10 to the power of 8 watt per meter to the power of 4 upon meter square C 2 equal to H C naught by k equal to 1.439 into 10 to the power of 4 micrometer Kelvin. Now this is the Planck's distribution what we have. So I implore that in your classes you spend enough time in distributing this Planck's distribution. So this is emissive power this is wave length area under each curve gives me the net emissive power of the black body at that temperature. This is 100 and this is 5800 why we have plotted 5800 because that is almost equal to the sun's temperature that is why it is called as here it is written as solar also. So in fact I would request that you should you should request your students to plot this in excel sheet we are not copy pasted this figure from any textbook we have plotted this in a grapher and drawn this graph. So this so if you plot it yourself you will feel the numbers much better than otherwise. So you have the emissive power and wave length and there is always a maxima if I connect that maxima you get lambda maximum into t equal to 2897.8 micrometer Kelvin. So this is what is called as Wien's displacement law. So he is Professor Wien and if I integrate this with respect to all wave length covering all thermal radiation wave length I will be getting sigma t to the power of 4 where sigma is 5.67 into 10 to the power of minus 8 watt per meter square Kelvin to the power of 4. So that is Stefan Boltzmann law in fact in fact there is a paper on the history of Stefan and Boltzmann I will I cannot upload the paper myself but I will try to make a notes please note this down I will try to make a notes on Stefan Boltzmann but I can give the reference. So that might be available in if the journal paper is available at your end download that paper and read it gives us the historical perspective of how the Stefan has done the Kharu fitting it is a beautiful paper I would recommend that all teachers should read that paper if you do not have that paper you send me you send me a you send me an I will make the notes and send because I cannot upload the paper PDF paper I am not supposed to give because of copyright issues I cannot give that journal paper if you can download from your end you can always download so then we studied band emission f of 0 lambda equal to e lambda, b d lambda 0 to lambda upon sigma t to the power of 4 so if I put that I represented that in terms of lambda t and we said that if I have to know the fraction of the energy or the fraction of the emissive power which is emitted within a band of 0 to lambda 1 if I need that I have defined what is called as f of 0 lambda this is represented in terms of lambda t and I have i lambda, b lambda t upon sigma t to the power of 4 and this is i lambda, b lambda t upon i lambda, b at lambda maximum, t okay so with this we solved a problem and we appreciated the importance of this table very much and then we went ahead and defined 4 emissivities that is this is the emissivity in general is the radiation emitted by a surface upon radiation emitted by a black body at the same temperature so that is why the emissivity the spectral emissivity here you see the emissive power of a real body is lower than the black body number 1 and number 2 is that it is having directionality unlike a black body so that is the real surface. Now we defined 4 emissivities one was spectral directional emissivity and total directional emissivity and spectral hemispherical emissivity and total hemispherical emissivity so we said that whenever directional dependence is there directionality I always handle it by intensity whenever directionality is not there whenever I have averaged the intensity over all directions then when there is no directional dependence I handle emissive power that is what we see here whenever directional dependence is there spectral directional emissivity you see theta comma phi I am using I I lambda comma E lambda theta comma phi t upon I lambda comma B lambda t okay so next is I get total directional emissivity that is I have again directionality so that is why I have intensity again so then spectral hemispherical emissivity here I have come back to emissive power because I have integrated over theta comma phi emissive power at lambda given by lambda at lambda comma t upon E lambda comma B lambda t we related spectral hemispherical emissivity with the directional emissivity so when we do that we get some equation like this and the next one is total hemispherical emissivity that is emissivity equal to E of t upon E B of t and of course you can represent this as epsilon lambda lambda t E lambda comma B lambda comma t this is what we had defined just little while ago that is this so if I substitute this this is what I get applying this relation I solved a problem this is what applying this is the application of that relation I solved a problem where in which I have taken for this bandwidth that is 0 to lambda 1 I have epsilon 1 and between lambda 1 to lambda 2 it is epsilon 2 and between lambda 2 to infinity it is lambda 3 that is why I get epsilon at what is this I said average emissivity what is this actually this is spectrally averaged perhaps if it is nothing is mentioned perhaps it is perhaps it is hemispherical emissivity it is averaged that is why we have put average so do not get carried away average it is actually spectrally we are averaging right now and it is perhaps the hemispherical emissivity so I get epsilon 1 f 0 lambda 1 t epsilon 2 f lambda 1 to lambda 2 plus f plus epsilon 3 f lambda 2 to infinity how do I get f lambda 1 to lambda 2 it is f 0 to lambda 2 minus f 0 to lambda 1 if you see one another thing I want to tell is we all think through images another insight what I have learned with time is that whenever I tell something what should come in the back of my mind is the image so when I say f lambda 1 to lambda 2 equal to f 0 to lambda 2 what is the image which should come to my mind is that my image should be I should visualize that and tell otherwise perhaps I am not telling with that feel that is this is the emissive power and this is the lambda when I say lambda 1 to lambda 2 this is lambda 2 and this is lambda 1 so that is f of lambda 2 to lambda 1 mean it is f of 0 to lambda 2 minus of f of 0 to lambda 1 so the point is what I am trying to say is we all think through pictures actually see that is what always everyone tells see when I always take this example that is whenever I remember my mother my mother's face comes to my mind so whenever I remember a concept a figure should come to my mind then only I have understood that concept if I cannot if I cannot get an image when I see a concept then perhaps I have not understood that concept so whenever a concept I explain it should be through an image and that image should be recorded in my mind if no image is recorded in my mind I have neither I have not transmitted that concept to my student and nor I have understood that concept myself so we have to my point is we have to transmit concepts through images through figures through figures through figures figures tables graphs these are the ones which we will remember very easily you see I think as teachers you all appreciate you may not remember these names of your students but definitely you remember their faces when it comes to you will say oh I have taught you but you will vaguely remember him but you will not remember his name that is precisely what I am saying so we all remember images we may not remember exact relation but we will remember concepts through images that is what that is what we need to we need to emphasize while teaching. So that is what we did epsilon 1.3 epsilon 2.8 and 0.1 we did that integration and we get we got the value the total emissivity total hemispherical emissivity we got it as 0.521 so there is another problem I am sure many enthusiasts would have solved that problem yesterday night so now let us get move on to how does real surfaces do not emit radiation now real surfaces do not emit radiation in a perfectly diffuse manner because they are not black bodies they have directional dependence so whatever grass I am flashing I am not going to reason them out because it is quite difficult to reason them out I will attempt to reason them out in the second half of today's lecture so please do not ask me questions for now why is emissivity increasing decreasing either with temperature or with direction all that I can say for now is that they are all dependent on electromagnetic permeability and electric permittivity okay so they are dependent on that whether it is a solid liquid gas so it is they are all dependent that is emissivity transmissivity reflectivity absorptivity all these are dependent on electrical permittivity electrical conductivity magnetic permeability and the charge of the electron so with and the velocity of speed a velocity of the electromagnetic wave in that medium if you remember I had put c equal to c0 by n what is that n what is that n refractive index so we are going to define in the second half refractive complex refraction index equal to refractive index minus ik where is absorptive index so this n and k that is what is that I said complex index of refraction is given by n minus ik that is m equal to n minus ik where n is refractive index which we have studied through Snell's law I will touch that in the afternoon k is the absorptivity index this n and k are related by are related are related to electrical permeability and electrical permittivity and magnetic permeability I do not remember I do not remember what is the notation for magnetic permeability electrical permittivity and magnetic permeability okay so why am I telling all this epsilon reflectivity transmissivity absorptivity they are all functions they are all functions of this n and k so that is what I am trying to say I will for simple cases I will try to give you relations between epsilon and n and k in the second half of today I should not get into that now because I have to cover that is little as teachers we should know little bit although I also do not know completely but little bit whatever I have understood from modest I am going to explain you in the second half but now let us move on what we teach in the undergrads so emissivity is a function of direction so this figure demonstrates that the real surfaces are not diffuse surfaces for conductors see I why I said electrical permittivity and magnetic permeability is because this conductors have different electrical permittivity okay so that will decide my emissivity and this emissivity is having preference to particular direction for conductors and nonconductors this is a general way it is not that for all nonconductors it is going to be like that generally for nonconductors emissivity is higher than that of conductors and nonconductors emissivity increases continuously with theta and this is and here theta direction is shown okay theta is 0 means it is normal okay okay so with this let us move on so that is what is called as when theta equal to 0 that is what is called as normal emissivity because it is normal to this surface so now temperature dependence like thermal conductivity here also we have temperature dependence the total normal emissivity as a function of temperature if you see you get that for tungsten it is increasing stainless steel it is increasing aluminum oxide it is decreasing heavily oxidized stainless steel it is decreasing again I will take the recourse of permeability so okay so I have not explained you why it is increasing decreasing I have just stated that emissivity is a function of temperature now and you can see that emissivity of polished metals is generally lower than emissivity of unpolished materials see yesterday for one of the questions of Prof. Vivek I was answering that a diffuse surface a diffuse surface will have I emissivity that is an unpolished is towards diffuse that is there is no glaze if you see in fact in fact if you see the blackboard most of our blackboards which we use they are all diffuse actually because of putting chalk over it again and again they have become diffuse they are not polished so blackboard will be more will be having higher emissivity than the blackboard which I started using on the first day on the first day so polished metals so if you want to increase the emissivity polished metals should not be used they should be used unpolished metals and another thing I do not know whether you have noticed or not so we I think I will come to that example little later on that is I wanted to explain the aluminum foil thing aluminum foil thing I will come to that little later on so these are oxidized metal and as you see here you see human skin and water water is emissivity one I understood this in a hard way see actually one of a one day I had a wonderful student by name Prabhu he was one of the best students I had and he was doing some two phase slow experiments and one we had to heat the water in a tank and we were supposed to take the tank temperature that is the water temperature in the tank to reach to 50 to 60 degree Celsius and then do the experiments by maintaining the temperature at 50 or 60 degree Celsius so I went to lab one day and every day I used to check the temperature of the water in the tank so that I put off the heater or put on the heater by checking with the thermometer but one day I went to the lab and Prabhu was measuring with the thermal camera that is there is a thermal gun see I do not know how many of you why I am taking this example because I want to explain you how does the thermal gun works also so there is a thermal gun nowadays what is that Taiwan make Taiwan thermal guns are available just for 5000 6000 rupees if you can afford I would request you to purchase thermal gun it is actually called as thermal infrared infrared gun also few people loosely call it as camera also although it is not or they call it as thermal infrared laser also okay these are various names there is fluke make if you are very much interested I can give you the address and the supply person of this fluke make you get a simple thermal camera fluke is little expensive means it comes to around 25 to 30,000 rupees if you cannot afford that much we get Taiwan make Taiwan make thermal cameras also so this Taiwan make thing we had which is hardly 4000 5000 rupees Prabhu was just measuring the emissive measuring the temperature of the water with that gun he said temperature is 40 degree Celsius without putting thermometer I used to put the hand gloves and put the thermometer because water was hot and things like that so from Prabhu I learnt that emissivity of the water is one how did I learn that emissivity of water is one because in a thermal gun I should I should fix the emissivity then only I will get the temperature okay so if I know the emissivity of a surface the thermal gun gives me the temperature so on that day he was getting directly the temperature why because the emissivity of water emissivity of water is one emissivity of water is one so he said sir thermometer reading and the thermal gun reading are matching he also did not know that emissivity of water is one but they are matching from that we realize that emissivity is one we refer back to books and we saw that emissivity of water is indeed one in fact yesterday you have taken emissivity of ice also as one okay so the point is what I want to tell is a thermal camera or a thermal gun measures measures the heat flux that is the thermal radiation what is the thermal radiative heat flux what is the thermal radiative heat flux we have Stefan Boltzmann emissive power Stefan Boltzmann law says that it is sigma t to the power of 4 it gives it thermal camera if this is my thermal camera the input is radiative flux that is e that is sigma epsilon t to the power of 4 if I have a surface if it is emitting if I aim my gun towards the surface it is going to capture sigma epsilon t to the power of 4 remember this is watts per meter square watts per meter square that is why I call this is radiative flux so now this gives this gun gives it gets the voltage output this voltage output actually how does it get voltage output again it is a simple resistor which is there inside because of this radiative heat flux it gets this resistor gets heated up because of this heating up the resistance changes and that is change in the resistance is perceived as a change in voltage okay so this is what is called as actually bolometer there is this is what is called as bolometer that is bolometer essentially consist a resistance and when radiative heat flux is incident on the resistance this resistance the temperature of this resistance increases so this change in the temperature is perceived as a change in the resistance which is perceived as a change in the voltage which is what we measure and this voltage output is a measure of temperature how can I get temperature can I get temperature directly here no only if I know the emissivity if I plug in emissivity in that camera it will give me temperature okay so what is thermal camera then what is thermal camera thermal camera is a combination of multiple bolometers that is mult is a combination of micro bolometers thermal camera micro bolometers micro bolometers that is in a thermal camera you have if you purchase a thermal camera or what you most of us have cameras with us in our mobiles how do you specify a camera megapixels you say 10 megapixels I have 20 megapixels I have similarly thermal camera also has pixels pixels means what it is it is made of multiple squares my camera is capturing my image using multiple squares multiple squares so 10 MB pixels means that many squares I have to make my image in fact my image is being transmitted to you through thousands of pixels tens of thousands of pixels that is how each square is a combination to make my image similarly to get a thermal image there is typically if you go to market you get 320 by 240 pixels 320 by 240 pixels thermal camera so this 320 by 240 pixel thermal camera is that means along this axis you may have 320 pixels and here you have 240 pixels that means you have 320 on this direction and 240 squares in this direction so that many pixels you are going to form when you are making a picture thermal picture so each pixel is what here each pixel is a micro bolometer each pixel each pixel is a micro bolometer and each micro bolometer has to be separated from the another micro bolometer otherwise resistances will become one resistance will talk to another resistance so they have to be insulated that is where micro machining comes into picture this is micro in size micro on size this complete micro bolometer will be hardly one centimeter by one centimeter within that one centimeter by one centimeter they have to embed 320 by 240 micro bolometers and again they have to be separated by insulators electrical insulators so that is what is a thermal camera made of so coming back if you have a thermal camera in a thermal camera what is that it will it will give you radiative heat flux sigma epsilon t to the power of 4 it will give you if you know the emissivity of a body that is you take a black paint you take a sheet you apply black paint with lamp that is candle suit that is it you get an emissivity almost as close as 0.98 0.99 of course it cannot be used for high temperatures because lamp black will vanish at high temperature but at room temperatures are nearly up to 70 to 80 degree Celsius lamp black there is no problem so for that body you can take epsilon so then you can from if you get the emissivity if you fix the emissivity thermal camera directly gives you the temperature everyone keeps asking me in our lab if you because we have thermal camera they keep asking us ok you have thermal camera you get me the thermal camera will measure the temperature no it is not like that I should be knowing the emissivity if I know the emissivity only we can measure the thermal camera someone will come and ask me I have a tool rotating and machining is going on I want to measure the temperature come and measure because you have thermal camera that is the perception we have no thermal camera does not give me temperature if I know emissivity only I can measure the temperature now why did I tell all the story I told the story because I wanted to explain you how to measure the emissivity have I explained it I have explained it implicitly let me explain it explicitly that is what do I do I take a thermal camera and now I take a thin metal foil this is thin metal foil thin metal foil and I heat this metal foil there are multiple ways of heating metal foil you can take you can make an iron box type heater using the nichrome heater you can put the nichrome heater behind of course before the heater there should be insulating material and after that also insulating material if you have and if you heat this the metal plate get heated up or you can take the thin metal foil and directly give dc power supply let us say it is stainless steel foil you give directly dc power supply how do you give dc power supply why is it made thin metal foil because I need to increase its resistance r equal to sigma l by a if my cross sectional area is less my resistance will go up still if I have to give direct dc power supply here current will be very large voltage will be very less it is safe way my students can touch the foil I can touch the foil you can touch the foil nothing will happen so because the major culprit in electricity is voltage not electric electrical current okay if the current is high also no problem even if it is 400 amps no problem as long as the voltage is 1 or 2 volts I can touch it there is no problem okay so that is what here we do if the resistance is high current will be very large voltage will be very less you can put a transformer and achieve this inlet to the transformer you can have 220 volts and 15 amps outlet of the transformer you can have high current but low voltage that is one way or you can get directly dc power supplies nowadays what 5000-10000 rupees we will get very good dc power supplies you do not need large power if you take some such dc power supply or ac supply and give directly if it is ac supply it has to be given through transformer or it has to be directly dc supply dc supply means you have to purchase a dc power supply and connect to our ac supply and get the dc okay so if you do any of that why am I doing all the circus because I want to maintain this stainless steel foil at certain temperature at a constant temperature let me say I maintain that at a constant temperature now I will put a thermocouple behind now I put a thermocouple why to get the temperature of this foil so thermocouple temperature I get now I will I will use the camera I will use the camera and in the camera there is a provision that I can change the emissivity I will keep on changing the emissivity until my camera's temperature matches with the temperature indicated by the thermocouple that emissivity what I have set in the camera will give me the emissivity of the emissivity of the surface I hope you have all understood so point is how do I measure emissivity this emissivity is not spectral emissivity this emissivity is perhaps a sort of total hemispherical emissivity because I am covering it I am seeing the camera from all directions so it is sort of hemispherical number one and it is it is not spectral because why it is not spectral because this camera is typically the cameras are between three micrometer to fifteen micrometer typical thermal guns whatever you purchase they are between three to fifteen micrometers why because we you and I know thermal radiation is within this range okay so this range is covered for spectrally averaged between three micrometer to fifteen micrometer in all directions that is total hemispherical emissivity is measured by a simple thermal camera you if you purchase 5000 rupees worth Taiwan make thermal gun you can measure the emissivity you can cook this whatever setup whatever I told now you can build this experimental setup in your lab and cook up one more emissivity experiment I know you measure emissivity in a little different way I when I coordinate when I interacted with the coordinators in the coordinator workshop they have a setup similar to the one which we have based on the heat flux they will measure the they will keep they will take a black body and they will take an ordinary black body ordinary body try to maintain the same heat flux by operating or by changing the temperature and see that at what temperature both the heat fluxes are same and then equate that and then you get the emissivity apart from that this is another elegant way of measuring thermal measuring emissivity this way we would have introduced the student to the thermal gun another application which you have noticed or not this example I always take why because this is very close and we would have all of us would have noticed this that is when swine flu was observed you in NDTV and CBN IBM they were flashing in the airports people were holding the thermal camera people were holding thermal camera and they were seeing the people who are coming through the exit port that is they were seeing whoever is having temperature higher than 37.5 normal temperature they were screened they were taken to the doctor and asked for that means they were trying to see whether a person is having fever or not through the thermal camera the beauty of thermal camera is that it is a non-intrusive measurement now the person who is being measured also does not know that he is being measured okay so such a and another advantage is that the emissivity of the surface is one so I do not have to plug in any parameter in my thermal camera so thermal camera has some tremendous applications in real life but we should keep in our mind what are the what are the limitations of the thermal camera thermal camera does not give temperature that is what we need to appreciate okay so with this let us move on I digressed because I wanted to explain you how does one measure emissivity in fact if you want to get a perfect black body there is there is a paint called pyromark there is a paint called pyromark they have very nicely I do not know the composition of this paint but this paint is a very good paint which can sustain blackness that is the emissivity and absorptivity are closer to one even at high temperature of 1000 degree Celsius but only thing is that we need to bake it that is we need to keep the pyromark after painting for we have to spray paint we cannot we cannot paint it by brush we have to spray paint it number one and number two we have to what is that we have to bake it under furnace for keeping it at 200 degree Celsius for let us say 4 to 5 hours that is that is what is what is called as baking if you bake it with the pyromark under a furnace this will give me emissivity absorptivity closer to one even at high temperatures okay so this also you can do in your lab by putting this okay coming back so these are the range of the emissivities what we get for various materials and similarly we have absorptivity so that is absorptivity and reflectivity and transpecivity this we have defined in the yesterday's class and these are the various definitions I hope you have all gone back and brushed up yourself all these definitions remember that I am using whenever I am using absorptivity I am using the notation I because I have to I have to take care of intensity incident on to my surface so if you note that difference all other definitions are going to be same and absorptivity is a function of temperature and another important thing yesterday one of the professors during interaction asked and I said I am postponing this question that is emissivity sorry absorb emissivity depends on the surface temperature but absorptivity is almost if not completely independent of surface temperature but what does it absorptivity depends on absorptivity depends on the temperature of the source at which the incident radiation is originating okay so why because you see in this example which is shown here there is a house the radiation on to the house is from sun from sun which is sitting at 5788 degrees Celsius and from trees which is sitting at 300 Kelvin okay so what is the emissivity what is the absorptivity of 3.9 what is the absorptivity of sun 0.6 sorry absorptivity of sun is a wrong term absorptivity of my house because of the incident radiation from the sun or because of the incident radiation of the tree because of the incident radiation of the trees the absorptivity of my building is 0.9 on the other hand absorptivity of my building because of the incident radiation of the sun is 5780 absorptivity how have I find absorptivity it is the it is dependent on incident radiation that means it should be dependent on the source not the sink that is the material which is emitting it is not that. So it is dependent on the incident rate it has to come from the definition it has to come from definition if you see how do I define absorptivity absorptivity is the net irradiation on to my surface. So that means it has to depend on the source. So you can answer your students that absorptivity is dependent on the source because it is coming from the definition. So that is how we can answer why is absorptivity dependent on the source temperature but not the sink temperature. So reflectivity similarly we can define reflectivity and I only take reflectivity for explaining reflectivity example yesterday also I took this example in a flask I said that my flask material if you opened it it is very flashy why because I want to have very high reflectivity very high reflectivity and I think you have all noticed we use aluminum foil for packing our chapatis when we go in trains when we are going travelling in train we pack chapatis in and even in train we are served with chapatis which are rolled in aluminum foil why those why aluminum foil why not some other plastic cover why because aluminum foil is having high reflectivity very high reflectivity. So coldness that is against coldness no coldness can seep into my chapatis that is the point that is the point. So no heat transfer is there from my chapatis to outside so that is why we can be high reflectivity example can be quoted taking aluminum foil okay even on even if you see the if you take a pipeline and if you have put thermo wool you have put thermo wool around a pipeline now thermo wool is put to basically control the conduction losses and convection losses. So you have put the thermo wool now over and above this thermo wool you would have seen aluminum foils wound on that okay very high reflective foils are wound on that why because reflectivity is to be avoided okay I mean high reflectivity should be there there is no radiation losses from the thermo wool to the outside atmosphere is that okay okay so with this we have the reflectivity the reflectivity is defined there are two ways of looking reflectivity one is a diffuse surface another one is specular specular is like mirror that is whatever angle of incidence is equal to angle of reflection so if that is the case then it is called specular otherwise it is diffuse that is it is equal in all directions so we have trans similarly we have transmissivity all sorts of definitions spectral hemispherical total hemispherical and other definitions we can go ahead and define this is just I do not want to spend time here why leaf is green I think we all study this in plus two because it absorbs all other colors except that it emits only the green color I think we say this again and again so I think I will just solve this problem before I sign off okay so I have spectral hemispherical absorptivity this is the problem how does spectral hemispherical reflectivity vary with wavelength and what is the total hemispherical absorptivity of the surface if the surface is initially at 500 Kelvin and has a total hemispherical emissivity of 0.8 how will its temperature change upon the exposure to the irradiation so what is given I have been given the absorptivity what which absorptivity I have been given spectral absorptivity that is up to 0 to 8 I think if I am right this 0 to 8 it is having an absorptivity of 0.2 and from 8 to 10 let me see that I will be able to answer that now yeah 0 to 6 6 to 8 sorry the figure is not clear sorry about that 0 to 6 it is constant 6 to 8 it is increasing and 8 to infinity it is going constant so now irradiation is also having a distribution like that okay so that is 0 to 2.02 irradiation is 0 to 0.2 this is 0 to 2 and 2 to 5 it is 500 and 5 to 12 it is 500 again and 12 to 16 it is decreasing so this is irradiation so we will come back to that when we are solving so this is irradiation distribution is given and absorptivity distribution is given so taking that the question asked is find the spectral distribution of reflectivity and total hemispherical absorptivity and nature of the surface temperature range so if I this is my surface and surface temperature is having 500 Kelvin and emissivity is total hemispherical emissivity is given to be 0.8 and emissive power is emissive emissivity into eb and irradiation is alpha into g so alpha plus tau plus rho equal to 1 transmissivity of this surface is 0 so I get rho equal to 1 minus alpha so now rho equal to 1 minus rho lambda equal to 1 minus alpha lambda I have been given alpha lambda so at every wavelength if I deduct 1 minus alpha lambda I should be getting rho lambda that is what I have done here and I get rho lambda I get rho lambda using this distribution now what is the next that gives me spectral distribution of reflectivity is that okay now next is I have alpha lambda and g lambda given already now what is that I need to do total hemispherical absorptivity have I defined that yes I have defined that total hemispherical absorptivity is given by alpha lambda g lambda d lambda upon g lambda d lambda both integrated between 0 to infinity this is like the way we define total hemispherical emissivity similarly we solved a problem based on which we took different emissivities in different bands similarly we are taking different absorptivities in different bands so if I do that integration see here in this range both absorptivity and irradiation are constant that is 0.2 into g lambda d lambda between 2 to 6 2 to 6 during that time my g lambda is constant and then g lambda is constant at 500 between 6 to 8 but between 6 to 8 my alpha lambda is increasing okay and plus absorptivity is 1 for 8 to 16 that is where between 8 to 16 what do I have 8 to 12 it is constant and then from 12 to 16 it is decreasing that is what is accounted here so it is basically area under the curves so that integration I am doing if I do that integration I get total hemispherical absorptivity as 0.76 you please sit down over t break t break just do this integration I am just doing simple integration by taking area under the curves now what is the net heat transfer net heat transfer is alpha g you see alpha g minus e epsilon e b so if I do that alpha g minus epsilon sigma epsilon t to the power of 4 alpha we got 0.76 and g is how did I get g as 5000 how did I get g as 5000 the integration of g that is the area under this curve is 5000 so that 5000 if I substitute and 0.8 is the emissivity which has been given sigma and this is t what is this t surface temperature 500 to the power of 4 3800 minus 2835 I get 965 watts per meter square what does this mean it is coming out positive that means it is receiving more than a bit that means the temperature of my body should be increasing with time so the net heat flux to the surface is greater than 0 so therefore the surface temperature will increase with time I think there is another problem with the cover glass I am not going to do that here this is about transmissivity this problem was cooked to explain absorptivity and this problem is cooked to explain transmissivity so I would request you to solve this problem yourself and I will I will take may be one or two questions one question I will take before I sign off so yesterday we could not go to VJT I Mumbai so I am going to VJT I Mumbai please restrict your questions to today's topic or yesterday's radiation topic what was taught over to VJT I Mumbai for questions hello sir my question is if I am getting the radiation if I am getting the radiation from the sun it is long wavelength or short wavelength radiation and second question is if I am using the window for the home purpose I have the double glazed glass and one I have the single glazed glass okay so the whatever the radiation coming inside through the solar is high or low and it is which type of wavelength it is from the solar radiation I am getting whatever the radiation is short wavelength or long wavelength see if you see the question the question can be answered through Planck's distribution so let us see if we take two it is I think it is in radiation that means it should be there in this itself I am in radiation to itself so let us go to Planck's distribution so in fact okay so if I see the Planck's radiation so if you see the Planck's radiation what is solar radiation 5800 Kelvin 5800 Kelvin means if you see here the radiation where is it visible light region is between around 0.5 to 1 micrometer okay I do not know what you mean by short or wave large wavelength yes if I have to answer that way okay the solar radiation that way for any temperature short wavelength will have a higher emissive power compared to large wavelength so is in case of solar radiation the most of the energy is concentrated between 0.08 micrometer to maybe 1 to 5 micrometer okay so but then we cannot generalize like that but generally this is the wave length band which the solar radiation is occurring second question you had the second question was there is a double flare glass and a single flare glass how does the how do they work I have to look at the transmissivity patterns until I see the transmissivity patterns I will not be able to comment what I would request you is to look for the transmissivity distribution of the single flare glass and the double flare that is the answer for your question one more question sir you have just now given an example of aluminum foil that is wound on chapathis or pipes carrying hot fluids which are insulated can you just elaborate how these aluminum foils are going to reflect coldness and aren't they going to reflect the heat also that yeah they are going to reflect both cold and heat both cold and heat see in the first example of chapathi I do not want to lose the heat in the second example when I am doing when I am putting this aluminum foil may be on a hot water pipe which is let us say we have a hot water pipe and there is a flow taking place of the hot water in this pipe here I do not want to lose the heatness from my hotness of from my hot water here again aluminum foil avoids the coldness which is coming from the for cryogenic fluids also you use aluminum foil so it is no matter whether it is for heating application or cooling of cooling application for all reflective for avoiding reflection we do put aluminum foils is that okay I think I think we will move on we will move on professor Arun will take over and start off with Kirchhoff's law.