PHYS 101 Homework Questions

Question

The blackbody radiation emitted from a furnace peaks at a wavelength of 4.8  10^-6 m (0.0000048 m). What is the temperature inside the furnace?

Answer 1

Hi Meredith, I'm here to help! A blackbody, an object which absorbs all radiation which hits it, is a cornerstone of astrophysics. Physicists model many physical objects after blackbodies, such as stars or, in this case, a furnace. Since blackbodies are such an important idea, there are some premade, prepackaged and very useful relationships associated with them.

One of the most important relationships is Wien's law, which relates the maximum radiation wavelength λ to the temperature T of a blackbody. In particular, they are inversely proportional:

λ = b/T

where b is Wein's constant and is equal to b = 2.898...×10⁻³ m⋅K.

This problem asks us to find T when we know λ. Therefore, our steps are to solve for T algebraically by multiplying both sides by T and dividing both sides by λ. This will get us here

T = b/λ.

Lastly, we substitute λ = 4.8 × 10^-6 m to get T = 604 K.

Please let me know if you have any questions!