In a Carnot engine if the work done during isothermal expansion is $25 \%$ more than the work done during isothermal compression, then the efficiency of the engine is

The work done to increase the volume of 2 moles of an ideal gas from V to 2 V at a constant temperature $T$ is W . The work to be done to increase the volume of 2 moles of the same gas from 2 V to 4 V at the same constant temperature $T$ is

If the given graph shows the logarithmic values of pressure ( $p$ ) and volume ( $V$ ) of an ideal gas, then the ratio of the specific heat capacities of the gas is

The internal energy of one mole of a rigid diatomic gas at absolute temperature $T$ is