$A$ black body emits energy at the rate of $1 \ cal/cm^2 \cdot s$ at a temperature of $127^{\circ}C$. Find the rate of energy emission at a temperature of $527^{\circ}C$ in $cal/cm^2 \cdot s$.

The rate of emission of radiation of a black body at $273^{\circ} C$ is $E$. What will be the rate of emission of radiation of this body at $0^{\circ} C$?

Assuming the sun to have a spherical outer surface of radius $r$,radiating like a black body at temperature $t^{\circ} C$,the power received by a unit surface (normal to the incident rays) at a distance $R$ from the centre of the sun is,where $\sigma$ is the Stefan's constant.

The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$,the power radiated by it becomes $nP$. The value of $n$ is

The rate of radiation of a black body at $0^{\circ} C$ is $E \text{ J}s^{-1}$. The rate of radiation of the black body at $273^{\circ} C$ will be

$A$ small object is placed at the center of a large evacuated hollow spherical container. Assume that the container is maintained at $0 \ K$. At time $t = 0$,the temperature of the object is $200 \ K$. The temperature of the object becomes $100 \ K$ at $t = t_1$ and $50 \ K$ at $t = t_2$. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio $(t_2 / t_1)$ is: