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

If the wavelengths of maximum intensity of radiation emitted by two black bodies $A$ and $B$ are $0.5 \mu \mathrm{~m}$ and 0.1 mm respectively, then ratio of the temperatures of the bodies $A$ and $B$ is

Water of mass 5 kg in a closed vessel is at a temperature of $20^{\circ} \mathrm{C}$. If the temperature of the water when heated for a time of 10 minutes becomes $30^{\circ} \mathrm{C}$, then the increase in the internal energy of the water is (Specific heat capacity of water $=4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ )

A Carnot engine $A$ working between temperatures 600 K and $T(<600 \mathrm{~K})$ and another Carnot engine $B$ working between temperatures $T(>400 \mathrm{~K})$ and 400 K are connected in series. If the work done by both the engines is same, then $T=$