Blackbody radiation

let's talk about the blackbody radiation spectrum this was one of the most important things well a lot of important things came out of the 19th century but this was a very very very important thing that came out of the 19th century so here's the idea when things are in thermal contact what that means is that they're bumping into each other having collisions and sharing energy so if I've got a hot liquid and a cold liquid and I pour them together then the hot liquid is going to give some of its energy to the cold liquid so the cold liquid will get hotter and the hot liquid will get colder until they're at the same temperature and that's what thermal contact does now when they get into the same temperature that's thermal equilibrium the easy way to think about thermal equilibrium is everybody gets his share alright so when you're in thermal equilibrium all the atoms get the same amount of energy provided that they're using it there's all these little rules and I don't want to talk about right now but you can think about it that way so what about light I mean if I'm talking about atoms and they're interacting with each other atoms consist of electrons and nuclei and those things are charged so they ought to interact with the electromagnetic field so that means that they ought to be able to give some energy to electromagnetic waves so doesn't like get to play yes light gets to play and that's a major major thing because what that means is that everything that has a finite temperature everything in order to be in thermal equilibrium it's got to give some of its energy to light and of course what does light do when you give it energy it leaves it's not just going to sit around it's not you know attracted to the matter it doesn't care it's just going off a light bulb you turn it on well like leaves right so here's the idea every object that has a finite temperature is always radiating energy and this energy just comes from the thermal equilibrium it comes from the temperature itself so it's just radiating I'm radiating energy right now light energy so when we go ahead and measure the intensity of the light that's coming off versus the wavelength we get these real interesting curves the red curve is for a hot object the blue curve is for a cooler object notice that the red curve has a lot more energy a lot more intensity so that means that hotter objects give off a lot more light than cooler object still all right similarly we find that there's a little peak here notice that the cooler object peaks at a higher wavelength then the hotter object does so what that means is that as an object gets hotter it not only radiates more just overall it also starts to radiate at lower wavelengths so here this one wasn't radiating very much at that wavelength before but then we heat it up and now that becomes the maximum radiation alright so that's the way that blackbody radiation works these curves are extremely important they actually lead Planck to to propose photons that's where photons come from they come from this blackbody radiation spectrum now you can also understand this just kind of qualitatively if you've ever seen an electric range you turn it on turn it up to high and what happens how do you know it's hot well the filament is glowing right it starts glowing red so that's an indication that it's hot that means that the wavelength of peak emission has moved over far enough that you can actually see visible light see at my temperature right now I'm still radiating but I'm not radiating in the visible spectrum you've got to be pretty hot to radiate in the visible spectrum all right let's get quantitative on this there's two major major major formulas that are associated with the black body radiation formula no I'm not going to write up Planck's formula because it's kind of complicated but these are two things that are derived from it first one is the stefan-boltzmann law and that tells you how much energy per unit time or how much power is emitted by something that has temperature T so it tells us that power is equal to Sigma Sigma is the stefan-boltzmann law constant and you can measure it or you can calculate it from fundamental constants it's five point six seven times ten to the minus eight watts per meter squared Kelvin to the fourth all right now that unit of course you can get just by saying the power has to be watts and look what I'm multiplying by this is the area the surface area of the object obviously if it's bigger it's going to radiate more I mean think about the earth right the earth is radiating through every little piece of its surface area so it's a lot bigger than a beach ball so I would expect it to radiate a lot more energy so that's why the area is there then we have this e this is called the emissivity and you can basically think about it in terms of like greenhouse gases right the earth emits energy but then some of its bounced back so that would make the amount that it's actually emitting less okay so this is the emissivity all right it's between zero and one all right and then we have the temperature and what's weird about this is that the temperature is to the fourth power most of the time we just see things squared at best cubed but this is temperature to the fourth power and it's also the Kelvin temperature it is not degrees Celsius it's not degrees Fahrenheit certainly it's Kelvin temperature now as you remember from chemistry Kelvin temperature is Celsius temperature plus 273 now what's interesting about that is that room temperatures about 300 Kelvin so when you look at this number you say oh it's ten to the minus eight that's not very much power at all think about the fact that you're then going to multiply it by 300 to the fourth power all right so that actually makes this power fairly large um anyway so that's the first equation the second one is beens displacement law now this tells us how we can calculate the wavelength associated with maximum intensity if we know the temperature so he tells us that lambda max is equal to two point eight nine eight millimeter Kelvin and that's just a constant you could measure it in experiment divided by the temperature again that temperature has to be in Kelvin all right so let's just go ahead and do some examples so a human being has a body temperature internal body temperature of 98.6 degrees Fahrenheit that translates to 310 Kelvin so Dean's displacement law tells us that the maximum wavelength is nine point thirty five micrometers so this is a microwave you can't see it it's not visible it's in the far infrared all right but that's how thermal imaging works and that's how those heat goggles work you look at something and you're looking at this part of the spectrum and at this part of the spectrum all human beings are like light bulbs they're just radiating all right so we've got that for human let's get hot what about molten iron now you guys know that when you heat up iron enough that it starts to melt it starts to show that red starts to glow right so the temperature at which iron melts is eighteen hundred and ten Kelvin using beans displacement law we see that the maximum wavelength of emission is that 1600 nanometers now that's not visible it's infrared the the highest wavelength that we can see as human beings is about 700 nanometers so this is a little bit more than twice that however as you remember from the curves the maximum is not the only wavelength that's being emitted it emits at smaller wavelengths too and so it's just kind of beginning to glow that red that's the idea because that red is about 650 679 m eaters all right so that's molten iron what about the Sun the Sun has a surface temperature of about 5800 Kelvin that's very hot and when we use means displacement law we find a maximum wavelength emission of 500 nanometers that's like a Bluegreen so now you might ask if I look at the Sun it doesn't look like Bluegreen to be it ciello there's many reasons for that part of the reason is that when you look at the Sun you're actually seeing that whole spectrum and there's a lot more of the larger wavelengths than there are the smaller ones so you're averaging in all those Reds and all those oranges and all those things like that and that pulls what it looks like kind of further up the wavelength spectrum the other reason is that when you're looking up at the Sun you're really only seeing the light that hasn't been scattered away by the atmosphere if you look away from the Sun what do you see you see blue you see the sky that's because the majority of the light that's scattered by the atmosphere is the small wavelength stop so that stuff's going away what's left over the bigger wavelengths and that's why the Sun appears yellow when you look at it all right and then there's one other example that I wanted to give and this is the cosmic background radiation which is something that's very very very important to physicists all around the world essentially what happened was after the Big Bang things interacted for a while and then everything just kind of coalesced into atoms and everything and then the light that was remaining from the Big Bang decoupled from everything else because now everybody is neutral so the light is just going to propagate through the cosmic background radiation is the remnants today of that light that decoupled about 300,000 years after the beginning of the universe now when we measure the intensity of the different wavelengths that come in that cosmic background radiation we find a perfect black body spectrum in fact it's the most perfect one ever found in nature cosmic background radiation with a temperature of 2.7 to 5 Kelvin it's been cooling off since the Big Bang and by now it's called the 2.7 to 5 Kelvin anyway that's blackbody radiation spectrum one of the most important things to come out of 19th century physics and by - I can't do this with you - laughing back there so we had no that's not right three co-player points so have you ever gotten up a airplane that should be yeah dang it like five hundred degrees in here what all right when you're in chemistry class they're gonna be doing a lot of work you're gonna go funny ever so as an example we can consider like you've got a chain hanging from - um - fix

Channel: Brightstorm

Views: 98,777

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Keywords: physics, brightstorm, atom, quantum physics, object, finite temparature, emit, emission, light, wavelengths, temparature, studystorm

Id: XrAktUy3_3k

Length: 11min 39sec (699 seconds)

Published: Sat Nov 28 2015