The ratio of the efficiencies of two Carnot engines $A$ and $B$ is 1.25 and the temperature difference between the source and the sink is same in both the engines. The ratio of the absolute temperature of the sources of the engines $A$ and $B$ is

The heat supplied to a gas at a constant pressure of $5 \times 10^5 \mathrm{~Pa}$ is 1000 kJ . If the volume of gas changes from $1 \mathrm{~m}^3$ to $2.5 \mathrm{~m}^3$, then the change in internal energy of the gas is

When an ideal diatomic gas undergoes adiabatic expansion, if the increase in its volume is $0.5 \%$, then the change in the pressure of the gas is

To increase the rms speed of gas molecules by $25 \%$, the percentage increase in absolute temperature of the gas is to be