Anonymous
Anonymous asked in Science & MathematicsPhysics · 3 months ago

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?

_____K 

Thank you for your help in understanding this problem! :)

1 Answer

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  • NCS
    Lv 7
    3 months ago
    Favorite 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

    If you find this helpful, please select Favorite Answer!

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