The cooling rate of a sphere at $600\,K$ in an external environment of $200\,K$ is $R$. When the temperature of the sphere is reduced to $400\,K$,the cooling rate of the sphere becomes:

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

The area of a hole of a heat furnace is $10^{-4} \ m^2$. It radiates $1.58 \times 10^5 \ \text{calories}$ of heat per hour. If the emissivity of the furnace is $0.80$, then its temperature is ....... $K$.

Two spherical black bodies have radii $R_1$ and $R_2$. Their surface temperatures are $T_1 \ K$ and $T_2 \ K$ respectively. If they radiate the same power,the ratio $\frac{R_1}{R_2}$ is

$A$ wire of length $L$ and diameter $d$ is used in a bulb. The temperature of the wire is $T$ and the power radiated by the wire is $P$. Its emissivity is $e$ ($\sigma$ = Stefan's constant). (Assume that the emissivity of the wire material is the same at all wavelengths).

Two identical metal balls at temperatures $200^{\circ}C$ and $400^{\circ}C$ are kept in air at $27^{\circ}C$. The ratio of net heat loss by these bodies is: