Physics Help, thank you! :)?
A solid sphere has a temperature of 779 K. The sphere is melted down and recast into a cube that has the same emissivity and emits the same radiant power as the sphere. What is the cube's temperature in kelvins?
Thank you for your help in understanding this problem! :)
- NCSLv 73 months agoFavorite Answer
If the volumes are the same, then
a³ = (4π/3)r³
where a is the cube side length and r is the sphere's radius
a = 1.612r
area of the sphere is 4πr²
and the area of the cube is
6a² = 6*(1.612r)² = 15.6r²
The radiant power is the same for both and is directly related to the area and the temperature to the fourth power:
4πr² * (779K)⁴ = 15.6r² * T⁴
solves to T = 738 K
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