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

A rectangular slab consists of two cubes of copper and brass of equal sides having thermal conductivities in the ratio $4: 1$. If the free face of brass is at $0^{\circ} \mathrm{C}$ and that of copper is at $100^{\circ} \mathrm{C}$, then the temperature of their interface is