An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $P_A/P_I$ is $(C_P/C_V = \gamma)$.

$A$ gas of mass '$m$' and molecular weight '$M$' is flowing in an insulated tube with a velocity '$2V$'. If the flow of the gas is suddenly stopped and all the kinetic energy is utilized to compress the gas,the increase in the temperature of the gas is ($\gamma$ is the ratio of specific heats,$R$ is the universal gas constant).

An office room contains about $2000$ moles of air. The change in the internal energy of this much air when it is cooled from $34^{\circ} C$ to $24^{\circ} C$ at a constant pressure of $1.0 \text{ atm}$ is (Use $\gamma_{\text{air}} = 1.4$ and universal gas constant $R = 8.314 \text{ J/mol-K}$)

An ideal monoatomic gas is taken through a process $dQ = 2dU$. The molar heat capacity for the process is:

Carbon monoxide is carried around a closed cycle $abc$ in which $bc$ is an isothermal process as shown in the figure. The gas absorbs $7000 \; J$ of heat as its temperature increases from $300 \; K$ to $1000 \; K$ in going from $a$ to $b$. The quantity of heat rejected by the gas during the process $ca$ is ..... $J$. (in $; J$)

An ideal gas is subjected to a cyclic process $A B C D$ as depicted in the $p-V$ diagram given below. Which of the following curves represents the equivalent cyclic process?