The elastic energy stored per unit volume in terms of longitudinal strain $\varepsilon$ and Young's modulus $Y$ is

A large tank filled water to a height $h$ is to be emptied through a small hole at the bottom. The ratio of the time taken for the level to fall from $h$ to $\frac{h}{2}$ and that taken for the level to fall from $\frac{h}{2}$ to 0 is

A slab consists of two identical plates of copper and brass. The free face of the brass is at $0^{\circ} \mathrm{C}$ and that of copper at $100^{\circ} \mathrm{C}$. If the thermal conductivities of brass and copper are in the ratio $1: 4$, then the temperature of interface is

A monoatomic gas of $n$ moles is heated from temperature $T_1$ to $T_2$ under two different conditions, (i) at constant volume and (ii) at constant pressure. The change in internal energy of the gas is