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3 2T 0 0 Lo 4To 0Three 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

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 = Aa

Aa = 6L02

Surface area of cube B = Ab

Ab = 6(2L0)2

Ab = 24L02

Surface area of cube C = Ac

Ac = 6(3L0)2

Ac = 54L02

Energy radiated by cube A per second = Ea

Energy radiated by cube B per second = Eb

Energy radiated by cube C per second = Ec

Ea = \sigmaeAa(4T0)4

Ea = \sigmae(6L02)(4T0)4

Ea = 1536\sigmaeL02T04

Eb = \sigmaeAb(3T0)4

Eb = \sigmae(24L02)(3T0)4

Eb = 1944\sigmaeL02T04

Ec = \sigmaeAc(2T0)4

Ec = \sigmae(54L02)(2T0)2

Ec = 864\sigmaeL02T04

Eb > Ea > Ec

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

1) B

2) A

3) C

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