The graph below shows the radiation emitted by a perfectly...

The graph below shows the radiation emitted by a perfectly black body. Use the graph to calculate the temperature of the body. Energy Density x10¹³ (W/m²) 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 Wavelength (µm) On the graph above, sketch the curve you would expect to see for a cooler blackbody.

Transcript

00:01 Hi, am.

00:02 So in this question we are given a graph which shows the radiation emitted by a perfect black body.

00:09 So this graph has a shape which is very common.

00:15 So any black body will emit a radiation which looks roughly something like that.

00:24 And in the question we have to basically determine the temperature of the black body.

00:31 Notice that on the horizontal axis, we have the wavelength, so lambda in units of micrometers.

00:40 So what's important about this graph is to identify the peak.

00:45 So the location of the peak basically tells you at what wavelength the black body emits most of its radiation because on the vertical axis we have the energy density, so the peak would correspond to the most of the energy density being emitted.

01:01 At the wavelength of that peak.

01:03 So if we look at the graph, we see that roughly the wavelength that corresponds to the peak is about, let's say, 0 .55 microns.

01:18 Okay, so this is, let's call it lambda max because the energy density is maximum at this, this point.

01:24 So how can we use that to determine the temperature? so in order to do that, we have to use the so -called vin's law.

01:34 Or sometimes it's also called vin's displacement law, which says that the product between this lambda max and the temperature of the black body is actually a constant.

01:49 So this constant is 2 .898 multiplied by 10 to the minus 3.

02:00 And this is meters kelvin.

02:05 Good...

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