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Chapter 11: Problem 4

If the temperature of the sun is increased from \(T\) to \(2 T\) and its radius from \(R\) to \(2 R\), then the ratio of the radiant energy received on earth to what it was previously will be (A) 4 (B) 16 (C) 32 (D) 64

Short Answer

Expert verified
The ratio of the radiant energy received on the earth to what it was previously will be 64. Hence, the option (D) is correct.

Step by step solution

01

Write down the Initial Energy Expression

The initial energy is \( E1 = \sigma * 4 \pi R^2 * T^4 \) which is obtained using the formula for a sphere鈥檚 surface area substituted into the Stefan-Boltzmann law.
02

Write down the New Energy Expression

The new energy \( E2 \) when the temperature is doubled and the radius is doubled is \( E2 = \sigma * 4 \pi (2R)^2 * (2T)^4 \).
03

Compute the Ratio

The ratio \( E2/E1 \) is \( \sigma * 4 \pi (2R)^2 * (2T)^4 /(\sigma * 4 \pi R^2 * T^4) = 2^2 * 2^4 = 2^6 = 64 \)

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