A black sphere has radius '$$R$$' whose rate of radiation is '$$E$$' at temperature '$$T$$'. If radius is made $$R / 3$$ and temperature '$$3 T$$', the rate of radiation will be

A gas at normal temperature is suddenly compressed to one-fourth of its original volume. If $$\frac{\mathrm{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma=1.5$$, then the increase in its temperature is

About black body radiation, which of the following is the wrong statement?

For a gas, $$\frac{\mathrm{R}}{\mathrm{C}_{\mathrm{v}}}=0 \cdot 4$$, where $$\mathrm{R}$$ is universal gas constant and $$\mathrm{C}_{\mathrm{v}}$$ is molar specific heat at constant volume. The gas is made up of molecules which are