$A$ container has a small hole. At what temperature (in $K$) should it be maintained so that it emits $1 \ cal$ of energy per second per $m^2$?

Two spherical black bodies of radii $r_1$ and $r_2$ and with surface temperatures $T_1$ and $T_2$ respectively radiate the same power. Then the ratio of $r_1$ and $r_2$ will be:

An electric heater kept in a vacuum is heated continuously by passing an electric current. Its temperature:

At temperature $T$,the power radiated by a body is $Q$ watts. At the temperature $3T$,the power radiated by it will be (in $Q$)

The temperature of a black body is increased by $50 \%$. The percentage increase in the rate of radiation by the body is approximately: (in $\%$)

$A$ 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 $\sigma = 5.67 \times 10^{-8} \ W m^{-2} K^{-4}$):