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?


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

1 Answer

  • 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

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