A piece of metal has a weight of 49 g in air and 39 g in a liquid of density $1.2 \times 10^3 \mathrm{~kg} / \mathrm{m}^3 \mathrm{kept}$ at $32^{\circ} \mathrm{C}$. When the temperature of the liquid is raised to $42^{\circ} \mathrm{C}$ the metal piece has a weight of 40 g . If the density of the liquid at $42^{\circ} \mathrm{C}$ is $1.0 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$, then the coefficient of linear expansion of the metal is

A metal cooking pot has a base area of $0.2 \mathrm{~m}^2$ and thickness 2.0 cm . It boils water at a rate of $3.0 \mathrm{~kg} / \mathrm{min}$ when placed on a hot plate. The temperature of the part of the hot plate in contact with the pot is approximately [thermal conductivity of metal is $120 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}$, heat of vaporisation of water is $2 \times 10^6 \mathrm{~J} / \mathrm{kg}$ ]

A quantity of monoatomic gas undergoes a process in which pressure is changed linearly with volume. The pressure and volume are changed from initial value $\left(p_0 V_0\right)$ of final value $\left(3 p_0, 3 V_0\right)$. The heat absorbed by the gas during the process is

An ideal gas having initial pressure $p$, volume $V$ and temperature $T$ is allowed to expand adiabatically until its volume becomes 4 V , while its temperature falls to $\frac{T}{2}$. If the work done by the gas during the expansion is $\alpha p V$, the value of $\alpha$ is