If two soap bubbles each of radius 2 cm combine in vacuum under isothermal conditions, then the radius of the new bubble formed is

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

The efficiency of a Carnot's heat engine is $\frac{1}{3}$. If the temperature of the source is decreased by $50^{\circ} \mathrm{C}$ and the temperature of the sink is increased by $25^{\circ} \mathrm{C}$, the efficiency of the engine becomes $\frac{3}{16}$. The initial temperature of the sink is

The change in internal energy of given mass of a gas, when its volume changes from $V$ to $3 V$ at constant pressure $p$ is

( $\gamma=$ Ratio of the specific heat capacities of the gas)