Question

A black body at a temperature of ${227}^{\circ }C$ radiates heat energy at the rate $5cal/c{m}^2/s$. At a temperature of ${727}^{\circ }C$, the rate of heat radiated per unit area in $cal/c{m}^2$ will be:

• A. $500$
• B. $250$
• C. $80$
• D. $160$

Answer 1

Answer: (C)

Heat energy per unit time $R=\sigma Ae{T}^4$

Thus heat energy per unit area $R^{\prime }=\sigma e{T}^4$

$⟹$ $\frac{R_2^{\prime }}{R_1^{\prime }}=(\frac{T_2}{T_1}{)}^4$

Initial temperature of the body $T_1={227}^{o}C=(227+273)K=500K$

Final temperature of the body $T_2={727}^{o}C=(727+273)K=1000K$

$\therefore$ $\frac{R_2^{\prime }}{5}=(\frac{1000}{500}{)}^4$

$\frac{R_2^{\prime }}{5}=16$

$⟹R_2^{\prime }=80$ $cal/c{m}^2$