Blackbody Radiation: 100K to 1000K Energy Increase

[CaneAA]

Homework Statement

By what factor does the radiated energy increase when a blackbody changes temperatures from 100K to 1000K

a) 100
b) 6600
c) 1 x 10^ 4 <--- marked as the correct answer on the key.
d) 5.7 x 10^4
e) 1 x 10^6

Homework Equations

1) f(peak) = 5.88x10^10*T
2) E = hf

The Attempt at a Solution

By inspection, I see that if T increases by a factor of 10, the frequency will increase by a factor of 10 and so will the energy. So I'm getting that the answer is a factor of 10. I even plugged in numbers and I still get 10. I don't understand how they got that answer.

 

[WatermelonPig]

P is proportional to T^4. Factor = (T2^4)/(T1^4)

http://en.wikipedia.org/wiki/Blackbody_radiation#Temperature_relation_between_a_planet_and_its_star

 

[CaneAA]

I see, thank you. But how do you know they're referring to power and not energy? They don't mention power or rate of energy radiated.

 

[WatermelonPig]

If I told you that a mass was increased, then you would assume the gravitational force on it was also increased. It's a similar idea with energy and power.

 

[rwisz]

I would approach this problem by using the equations provided and understanding the concept of blackbody radiation. The key to solving this problem is to understand that the energy radiated by a blackbody is directly proportional to its temperature. This means that if the temperature increases by a factor of 10, the energy will also increase by a factor of 10.

Using the equation for peak frequency (f(peak) = 5.88x10^10*T), we can see that as the temperature increases from 100K to 1000K, the frequency increases by a factor of 10. This is because the temperature has increased by a factor of 10, and the frequency is directly proportional to the temperature.

Now, using the equation for energy (E = hf), we can see that the energy also increases by a factor of 10. This is because the frequency has increased by a factor of 10, and energy is directly proportional to frequency.

Therefore, the correct answer is a factor of 10, or option a). The other options are incorrect because they do not take into account the direct proportionality between energy and temperature.