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Question

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?

_____K 

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Answer 1

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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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