If the sun's surface radiates heat at $6.3 \times 10^7 \ W m^{-2}$,calculate the temperature of the sun assuming it to be a black body $(\sigma = 5.7 \times 10^{-8} \ W m^{-2} K^{-4})$.

The energy spectrum of a black body has maximum energy at a wavelength of $\lambda_0$. Now, the temperature of the black body is increased such that the maximum energy is obtained at a wavelength of $3\lambda_0/4$. By what factor will the power radiated by the black body increase?

$A$ black rectangular surface of area $A$ emits energy $E$ per second at $27^{\circ}C$. If the length and breadth are reduced to half of their initial values and the temperature is raised to $327^{\circ}C$, then the energy emitted per second becomes: (in $E$)

Two spheres of the same material have radii $1 \ m$ and $4 \ m$ and temperatures $4000 \ K$ and $2000 \ K$ respectively. The ratio of the energy radiated by them is .....

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:

$A$ black body is at $727^\circ C$. It emits energy at a rate which is proportional to