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 $\frac{V}{2}$. Sample $A$ is compressed isothermally while sample $B$ is compressed adiabatically. The final pressure of $A$ is

$A$ thermodynamic cycle takes in heat energy at a high temperature and rejects energy at a lower temperature. If the amount of energy rejected at the low temperature is $3$ times the amount of work done by the cycle,the efficiency of the cycle is

Two cylinders $A$ and $B$ fitted with pistons contain equal amount of an ideal diatomic gas at $303 \text{ K}$. The piston of cylinder $A$ is free to move and that of cylinder $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder $B$ is $63 \text{ K}$, then the rise in temperature of the gas in $A$ is: (in $\text{ K}$)

One mole of an ideal gas at initial temperature $T$ undergoes a quasi-static process during which the volume $V$ is doubled. During the process,the internal energy $U$ obeys the equation $U = a V^3$,where $a$ is a constant. The work done during this process is

$N$ moles of an ideal diatomic gas are in a cylinder at temperature $T$. Suppose on supplying heat to the gas, its temperature remains constant but $n$ moles get dissociated into atoms. Heat supplied to the gas is

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume ($\gamma = 1.4$ and $2^{-1.4} = 0.38$). The ratio of the final to initial pressure is (in $: 1$)