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If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q? ($\sigma$ stands for Stefan's constant)
A
$\left(\frac{Q}{4\pi R^2\sigma}\right)^{1/4}$
B
$\frac{Q}{4\pi R^2\sigma}$
C
$\left(\frac{Q}{4\pi R^2\sigma}\right)^{-1/2}$
D
$\left(\frac{4\pi R^2Q}{\sigma}\right)^{1/4}$
Detailed Solution
Stefan's law: power radiated by a black body $= \sigma AT^4$, with $A = 4\pi R^2$
In steady state the rate of energy production equals the power radiated: $Q = 4\pi R^2\sigma T^4$
$T = \left(\frac{Q}{4\pi R^2\sigma}\right)^{1/4}$
In steady state the rate of energy production equals the power radiated: $Q = 4\pi R^2\sigma T^4$
$T = \left(\frac{Q}{4\pi R^2\sigma}\right)^{1/4}$