First slide

Radiation

Question

If the temperature of the sun were to increase from T to 2T and its radius from R to 2R, then the ratio of the radiant energy received on earth to what it was previously will be

Easy

A

4
B

16
C

32
D

64

Solution

$E = {σAT}^{4} = σ (πR)^{2} T^{4} ∴ \frac{E^{'}}{E} = \frac{R^{'} \times T^{' 4}}{R^{2} \times T^{4}} = \frac{(2 R)^{2} \times (2 T)^{4}}{R^{2} \times T^{4}} = (2)^{2} \times (2)^{4} = 64$

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