Question

A black body at a temperature of $227 \,{}^\circ C$ radiates heat at the rate of $5 \, cal$ $ \, cm^{- 2} \, s^{- 1}$ . At a temperature of $727 \,{}^\circ C$ the rate of heat radiated per unit area in $cal \, cm^{- 2}s^{- 1}$ is

• A. $400$
• B. $80$
• C. $40$
• D. $15$

Answer 1

Answer: (B)

According to Stefan's law radiant energy emitted by a perfectly black body per unit area per sec ( $ie,$ emissive power of black body) is directly proportional to the fourth power of its absolute temperature ie $E \propto T^{4}$
$\Rightarrow $ $\frac{E_{1}}{E_{2}}= \, \frac{T_{1}^{4}}{T_{2}^{4}}$
$\frac{5}{E_{2}}= \, \frac{\left(\right. 273 + 227 \left.\right)^{4}}{\left(\right. 273 + 727 \left.\right)^{4}} \, $
$E_{2}=5\times \left[\frac{1000}{500}\right]^{4} \, $
= $ \, 5\times 16=80 \, cal \, cm^{- 2}s^{- 1}$