$A$ black metal foil is warmed by radiation from a small sphere at temperature $T$ and at a distance $d$. It is found that the power received by the foil is $P$. If both the temperature and distance are doubled,the power received by the foil will be:

Two spherical bodies of same materials having radii $0.2 \ m$ and $0.8 \ m$ are placed in the same atmosphere. The temperature of the smaller body is $800 \ K$ and the temperature of the bigger body is $400 \ K$. If the energy radiated from the smaller body is $E$,the energy radiated from the bigger body is (assume the effect of the surrounding to be negligible).

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:

The ratio of the energy of emitted radiation of a black body at $27^{\circ}C$ and $927^{\circ}C$ is:

$A$ thin steel square plate of side $10 \ cm$ is heated. The rate of energy emission from the heated plate is $1134 \ W$. What is the temperature of the plate in $K$? (Assume emissivity $\varepsilon = 1$ and $\sigma = 5.67 \times 10^{-8} \ W \ m^{-2} \ K^{-4}$)

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 ........ $cal$.