Question

Two bodies $A$ and $B$ are kept in an evacuated chamber at ${27}^{o}C$. The temperature of $A$ and $B$ are ${327}^{o}C$ and ${427}^{o}C$ respectively. The ratio of rates of loss of heat from A and B will be :

• A. 0.23
• B. 0.52
• C. 1.52
• D. 2.52

Answer 1

Answer: (B)

0.52

From Stefan's Law: $\frac{\Delta Q}{\Delta t}=\sigma eA(T^4-{T_o}^4)$

$\frac{\Delta Q_A}{\Delta Q_B}=\frac{{600}^4-{300}^4}{{700}^4-{300}^4}=0.52$

The ratio of rates of loss of heat can be found from the Stefan's equation. $T$ is given as $600K$ for $A$ and $700K$ for $B$, the $T_o$ is $300K$ in both the cases, on calculation the ratio of heat loss comes around $0.52$. thus the answer is B.