$A$ rectangular surface of a black body at $127^{\circ}C$ with dimensions $8 \ cm \times 4 \ cm$ emits energy at a rate of $E$. If the length and width are halved and the temperature is increased to $327^{\circ}C$,find the new rate of energy emission.

$A$ solid copper sphere of density $\rho$,specific heat capacity $C$ and radius $r$ is initially at $200 \ K$. It is suspended inside a chamber whose walls are at $0 \ K$. The time required (in $\mu s$) for the temperature of the sphere to drop to $100 \ K$ is ( $\sigma$ is Stefan's constant and all the quantities are in $SI$ units.)

Two black bodies at temperatures $327^{\circ} C$ and $427^{\circ} C$ are kept in an evacuated chamber at $27^{\circ} C$. The ratio of their rates of loss of heat are :

The total radiative power emitted by a spherical black body with radius $R$ and temperature $T$ is $P$. If the radius is doubled and the temperature is halved,then the radiative power will be

Two spherical bodies of radii $r_1$ and $r_2$ have surface temperatures $T_1$ and $T_2$ respectively. They radiate the same power. The ratio $r_1/r_2$ is . . . . . .

Two spherical black bodies have radii $r_1$ and $r_2$. Their surface temperatures are $T_1$ and $T_2$. If they radiate the same power,then $\frac{r_2}{r_1}$ is: