There are two samples A and B of a certain gas, which are initially at the same temperature and pressure. Both are compressed from volume v to $\frac{\mathrm{v}}{2}$. Sample A is compressed isothermally while sample B is compressed adiabatically. The final pressure of $A$ is

Two rods, one of aluminium and the other of steel, having initial lengths ' $\mathrm{L}_1$ ' and ' $\mathrm{L}_2$ ' are connected together to form a single rod of length $\left(L_1+L_2\right)$. The coefficients of linear expansion of aluminium and steel are ' $\alpha_1$ ' and ' $\alpha_2$ ' respectively. If the length of each rod increases by the same amount, when their temperatures are raised by $\mathrm{t}^{\mathrm{L}} \mathrm{C}$, then the ratio $\frac{L_1}{L_1+L_2}$ will be

Given that ' $x$ ' joule of heat is incident on a body. Out of that, total heat reflected and transmitted is ' $y$ ' joule. The absorption coefficient of body is

A diatomic ideal gas is used in Carnot engine as a working substance. If during the adiabatic expansion part of the cycle, the volume of the gas increases from V to 32 V , the efficiency of the engine is