Full transcript
0:00we can determine the temperature of the
0:02object using this formula right here is
0:05what we find is that the max wavelength
0:08is related to the temperature and it's a
0:11little confusing I know earlier we using
0:13temperature or the T as period now we're
0:18using this temperature unfortunately in
0:20science we only have a certain number of
0:21letters and so sometimes they get
0:23repeated so be a little careful you
0:25don't confuse and think this is a period
0:27notice the temperature if we can figure
0:30out the max wavelength where that peak
0:33hits we can determine the temperature of
0:36a distant star and this actually is how
0:38we determine the temperature of distant
0:40objects we can't go to that star and
0:41measure it so we look at the
0:43distribution of the radiation figure out
0:46the max wavelength and get the
0:48temperature and let's see an example so
0:51let's say we have a star and as it says
0:54here it's giving off radiation at 500
0:56nanometers and we're asked what is its
0:58temperature well the important thing to
1:00remember this formula is that this is
1:02three times ten days and six nanometers
1:05now if I give you a question and I will
1:08give you a question like this I'll
1:09always give you a nanometer so you don't
1:11have any weird things coming in that
1:13makes you have to do conversions so what
1:16we're gonna use is this formula to
1:17figure out the temperature and what we
1:20have to do is rearrange it to get
1:21temperature so multiply both sides by
1:23temperature goes over there divide both
1:25sides by this lambda max it goes there
1:27and we can think temperature is given by
1:30this formula we're given lambda max
1:32that's our 500 well and I guess I
1:37could've been more clear in this
1:38question actually saying that that is
1:39the maximum frequency I'll try to be
1:42clearer in assignments but we plug that
1:45in this is three times 10 to the 6 punch
1:49it in your calculator divide that by 500
1:52or three with six zeros after it divided
1:56by 500 and you should get 6,000 and the
1:59answer will always be in Kelvin so this
2:02would actually tell us that a distant
2:05star has a surface temperature the
2:07radiation is giving off is at 6,000
2:10Kelvin again
2:13a light from an incredibly distant
2:15object doing this allows us to figure
2:18out the temperature of that object and
2:20again it doesn't have to just be a star
2:22it could be a cloud of gas or whatever
2:25different object we are looking at in
2:28our in the universe now we do have
2:31another radiation long I talked about
2:34two because we also find that the amount
2:37of energy being radiated depends on the
2:41temperature and I'm actually gonna jump
2:42back a couple slides for a second
2:44because well you can see it right here
2:47as our temperatures increased the spike
2:51gets much much higher this over here is
2:54intensity or how much light we're
2:56getting in essence and you can see as
2:58our temperature increases it spikes
3:00quite a bit higher we're getting a lot
3:02more energy as a result so that's what
3:05this law is all about we find the amount
3:09of energy depends on the fourth power of
3:12the temperature so in other words as
3:14temperature increases the amount of
3:16energy increases very very very quickly
3:19okay let's take a look so I'm not
3:23actually gonna make you learn this
3:24formula there is a formula if you want
3:25you can reference the book but it has
3:27constant that's a really ugly units and
3:30number so I just want you to be able to
3:33understand this and apply it you know
3:35more generalized sense so in this case
3:37this is cape a question I'd ask we have
3:39a star that's putting out three times
3:42the temperature of the other star how
3:45much more energy does that relate to so
3:49star a has three times the temperature
3:51of star B how much more energy is it
3:53outputting well since there's two
3:56related to the fourth power of the
3:58temperature we just have to know how
4:00much hotter one is any other which were
4:02told is three times and we take the
4:04three and put it to the power of 4 or 3
4:07times 3 times 3 times 3 which is equal
4:11to 81 again you punch that in your
4:12calculator that would be our answer it's
4:14actually outputting 81 times the energy
4:18even though it's only 3 times hotter
4:21it's spitting out 81 times more energy
4:24than the other star