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Venus and Earth may be regarded as behaving as black bodies. The mean temperature at the surface of Venus is about 600 K and at the surface of Earth is about 300 K. Which of the following is the best estimate for the ratio \frac{\text{power radiated per unit area on Earth}}{\text{power radiated per unit area onVenus}} power radiated per unit area onVenus power radiated per unit area on Earth ​

Answer :

The best estimate for the ratio of Power radiated per unit Area on Earth and Power radiated per unit Area on Venus is 1/16. The correct option is D.

What is power radiated?

Power radiated is directly proportional to the fourth power of Temperature at the surface and also to the cross-section area.

P = σ A T⁴

For 600 K at Venus, σ A T⁴ = σ A (600)⁴

For 300 K at Earth , σ A T⁴ = σ A (300)⁴

Comparing, we get

[σ A (300)⁴/ σ A (600)⁴ ] = 1/16

Thus, the the best estimate for the ratio is 1/16. The correct option is D.

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