If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in internal energy of a mass of a gas when the volume changes from $$\mathrm{V}$$ to $$3 \mathrm{~V}$$ at constant pressure is

The molecules of a given mass of a gas have root mean square speed of $$120 \mathrm{~m} / \mathrm{s}$$ at $$88^{\circ} \mathrm{C}$$ and 1 atmospheric pressure. The root mean square speed of the molecules at $$127^{\circ} \mathrm{C}$$ and 2 atmospheric pressure is

Two black bodies $$\mathrm{P}$$ and $$\mathrm{Q}$$ have equal surface areas and are kept at temperatures $$127^{\circ} \mathrm{C}$$ and $$27^{\circ} \mathrm{C}$$ respectively. The ratio of thermal power radiated by A to that by B is

If heat engine is filled at temperature 27$$^\circ$$C and heat of 100 k cal is taken from source at temperature 677$$^\circ$$C. Work done (in J) is