A polyatomic gas with $n$ degrees of freedom has a mean kinetic energy per molecule given by (if $N$ is Avogadro's number )

The absorption coefficient value of a perfect black body is

A certain volume of a gas at 300 K expands adiabatically until its volume is doubled. The resultant fall in temperature of the gas is nearly (The ratio of the specific heats of the gas $=1.5$ )

The efficiency of a Carnot's engine is $25 \%$. When the temperature of sink is 300 K . The increase in the temperature of source required for the efficiency to become $50 \%$ is