Q131 / 155 · WBJEE 2016 · Physics

If the temperature of the Sun gets doubled, the rate of energy received on the Earth will increase by a factor of

  • A
    2
  • B
    4
  • C
    8
  • Correct answer
    D
    16

Solution

Suppose temperature of $\mathrm{Sun}=T$ When it is doubled, $T^{\prime}=2 T$ From law of radiation (Stefan's law) $$ E \propto T^{4}=\sigma T^{4} $$ $\sigma=$ Stefan's constant. $$ \begin{array}{l} E_{1}=T^{4} \\ E_{2} \approx(2 \Pi)^{4} \\ \frac{E_{1}}{E_{2}}=\frac{T^{4}}{2^{4} \cdot T^{4}} \\ E_{2}=16 E_{1} \end{array} $$

Hence, the correct answer is option: 'D'.

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