$A$ certain amount of gas of volume $V$ at $27^{\circ}C$ temperature and pressure $2 \times 10^{7} \; N m^{-2}$ expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use $\gamma = 1.5$)

$A$ gas is governed by an equation $V = \frac{aT^3}{P}$,where $P, V$,and $T$ are pressure,volume,and temperature of the gas respectively,and $a$ is a constant. If the temperature of the gas is doubled at constant pressure,then the work done by the gas is: (in $aT^3$)

Match the following:

Column $I$	Column $II$
$A$. Ratio of $\frac{\Delta Q}{\Delta U}$ in an isobaric process	$1$. $\frac{T_1}{T_1-T_2}$
$B$. Ratio of $\frac{\Delta Q}{\Delta W}$ in an isobaric process	$2$. $\frac{T_2}{T_1-T_2}$
$C$. Coefficient of performance of a refrigerator	$3$. $\frac{\gamma}{\gamma-1}$
$D$. Coefficient of performance of a heat pump	$4$. $\gamma$

Codes:
$A \quad B \quad C \quad D$

The figure shows the $P-V$ plot of an ideal gas taken through a cycle $ABCDA$. The part $ABC$ is a semi-circle and $CDA$ is half of an ellipse. Then,
$(A)$ the process during the path $A \rightarrow B$ is isothermal
$(B)$ heat flows out of the gas during the path $B \rightarrow C \rightarrow D$
$(C)$ work done during the path $A \rightarrow B \rightarrow C$ is zero
$(D)$ positive work is done by the gas in the cycle $ABCDA$

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is

For an ideal gas, a cyclic process $ABCA$ as shown in the $P-T$ diagram, when presented in a $P-V$ plot, would be: