Three cubes are made from the same material. As the drawing indicates, they have different sizes...

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3 2T 0 0 Lo 4To 0 Three cubes are made from the same material. As the drawing indicates, they have different sizes and temperatures. Rank the cubes according to the radiant energy they emit per second, largest first.

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Answer 1

Answer #1

Stefan boltzmann constant = $\sigma$

Emissivity of the material = e

Length of cube A = L₀

Length of cube B = 2L₀

Length of cube C = 3L₀

Temperature of cube A = 4T₀

Temperature of cube B = 3T₀

Temperature of cube C = 2T₀

Surface area of cube A = A_a

A_a = 6L₀²

Surface area of cube B = A_b

A_b = 6(2L₀)²

A_b = 24L₀²

Surface area of cube C = A_c

A_c = 6(3L₀)²

A_c = 54L₀²

Energy radiated by cube A per second = E_a

Energy radiated by cube B per second = E_b

Energy radiated by cube C per second = E_c

E_a = $\sigma$ eA_a(4T₀)⁴

E_a = $\sigma$ e(6L₀²)(4T₀)⁴

E_a = 1536 $\sigma$ eL₀²T₀⁴

E_b = $\sigma$ eA_b(3T₀)⁴

E_b = $\sigma$ e(24L₀²)(3T₀)⁴

E_b = 1944 $\sigma$ eL₀²T₀⁴

E_c = $\sigma$ eA_c(2T₀)⁴

E_c = $\sigma$ e(54L₀²)(2T₀)²

E_c = 864 $\sigma$ eL₀²T₀⁴

E_b > E_a > E_c

Ranking the cubes according to the radiant energy they emit per second (largest first),

1) B

2) A

3) C

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