First slide

Radiation

Question

If the temperature and radius of Sun are doubled and the average distance of earth from the sun is also doubled then power received by earth will be

Moderate

A

4 times
B

8 times
C

16 times
D

2 times

Solution

Power radiated from the surface of sun is given by $Q = σ \cdot (4 {πR}_{S}^{2}) \cdot T^{4}$
If r be the average distance of earth from the sun, then power received by earth is given by $P = \frac{Q}{4 {πr}^{2}} {πR}_{e}^{2}$
$∴ P \propto \frac{R_{S}^{2} \cdot T^{4}}{r^{2}} \Rightarrow \frac{P^{1}}{P} = \frac{{(2 R_{S})}^{2}}{{(R_{S})}^{2}} \cdot \frac{(2 T)^{4}}{T^{4}} \frac{(r)^{2}}{(2 r)^{2}} = 16$

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