Question

Two bodies $A$ and $B$ at temperatures ${327}^{\circ }C$ and ${277}^{\circ }C$ are kept in vacuum chamber at ${27}^{\circ }C$. Then ratio of their rates of loss of heat in a given time interval is nearly.

• A. 2 : 1
• B. 1 : 2
• C. 1 : 4
• D. 4 : 1

Answer 1

The correct option is A 2 : 1

Temperature of body $A$, $T_A={327}^{0}C=327+273=600K$

Temperature of body $B$, $T_B={277}^{0}C=277+273=500K$

Vacuum is maintain at temperature $T_m={27}^{0}C=27+273=300T$

Rate of loss of heat from body $A$,

$E_A=\sigma A({600}^4-{300}^4)$. . . . . .(1)

Rate of loss of heat from body $B$,

$E_B=\sigma A({500}^4-{300}^4)$. . . . . .(2)

from equation (1) and (2), we get,

$\frac{E_A}{E_B}=\frac{2}{1}$

$E_A:E_B=2:1$

Option A is correct.