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How do i calculate temperature for a planet when given its spectrum graph and the values on the graph are in nm?

 Oct 21, 2015
edited by Guest  Oct 21, 2015
 #1
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Have you looked in your textbook? What is the relationship between temperature and spectrum graph? If you have the formula, units don't matter, because you can easily convert from one to another.

 Oct 21, 2015
 #2
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It's with regards to a dwarf planet's temperature. 

the graph shows the spectrum of the dwarf planet, with the peak intensity hitting in between 10^2 and 10^3. 

I know that I have to use the Stefan-Boltzmann law:  σ T^4,  σ = 5.7 x 10^-8 watt/(m^2 x K^4), however T is in Kelvin and the values I'm given on the spectrum are in nm.

 

How would i figure out the temperature of this planet with the informatin I'm given? And how do i convert nm to K?

 Oct 21, 2015
 #3
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First of all, I think you mean "dwarf star"? 1m=10^9 nanometers. You may have to convert nanometers into meters by dividing by 10^9. Be sure NOT to confuse T in Kelvins by nanometers. The latter generally refers to wavelengths. Make all your units consistent.

 Oct 21, 2015
 #4
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no, I meant dwarf planet. That's exactly whats written on my assignment. to figure out the temperature, do i have to isolate t in the stefan law equation?

 Oct 21, 2015
 #5
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Why don't you state Stephan' Law and give us the variables that you are given. Will see what we can do. What does Stepahn's Law say as a formula?. Can you copy it from your book?

 Oct 21, 2015
 #6
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I stated stefan's law previously and the units I am given. 

 

I will restate them:

Stefan's law: σ T^4,  σ = 5.7 x 10^-8 watt/(m^2 x K^4)

 

 

T=temperature in Kelvin 

 

 

Graph values on x axis range from 

10^2 - 10^6 

 

Peak of graph is located between 10^2 & 10^3 

 Oct 21, 2015
 #7
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E=T^4 X 5.7 X 10^-8

10^2.5=T^4 X 5.7 X 10^-8

T^4=10^2.5 / (5.7 X 10^-8)

T=271.73 Kelvin-- I used 10^2.5 as the average graph peak. This T in Kelvin=-1.4 Celsius.

Well, what did you expect for the answer? Just wondering.

 Oct 22, 2015

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