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:

$A$ 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.

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 $1: 3$. If they radiate the same amount of heat per unit area per unit time,then the ratio of their temperatures $(T_1: T_2)$ is

$A$ black body radiates energy at the rate of $1 \times 10^5 \ J/s \cdot m^2$ at a temperature of $227^\circ C$. The temperature to which it must be heated so that it radiates energy at a rate of $1 \times 10^9 \ J/s \cdot m^2$ is:

Which of the following graphs correctly represents the relation between $\ln E$ and $\ln T$, where $E$ is the amount of radiation emitted per unit time from unit area of a body and $T$ is the absolute temperature?

The unit of Stefan-Boltzmann's constant $(\sigma)$ is: