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 bodies $A$ and $B$ at temperatures $T_1 \ K$ and $T_2 \ K$ respectively have the same dimensions. Their emissivities are in the ratio $16:1$. At $T_1 = x T_2$,they radiate the same amount of heat per unit area per unit time. The value of $x$ is

Two bodies $A$ and $B$ have emissivities of $0.01$ and $0.81$ respectively. The outer surface areas of both bodies are the same. Both bodies emit total radiant power at the same rate. The wavelength $\lambda_B$ corresponding to the maximum spectral radiance for body $B$ is $1.0 \mu m$. If the temperature of body $A$ is $5802 \ K$,then the temperature of body $B$ is .... $K$.

$A$ spherical black body with a radius of $24\;cm$ radiates $440\;W$ power at $500\;K$. If the radius were halved and the temperature doubled,the power radiated in watt would be

The temperature of a perfect black body is $727^{\circ}C$ and its surface area is $0.1\, m^{2}$. If the Stefan-Boltzmann constant is $\sigma = 5.67 \times 10^{-8} \, W/m^{2} \cdot K^{4}$,then the heat radiated in $1\, min$ is ........ $cal$.

$A$ very small hole in an electric furnace is used for heating metals. The hole nearly acts as a black body. The area of the hole is $200 \ mm^2$. To keep a metal at $727^{\circ} C$, the heat energy flowing through this hole per second, in joules, is (given $\sigma = 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$):