Three moles of an ideal gas $\left( {{C_P} = \frac{7}{2}R} \right)$ at pressure ${P_A}$ and temperature ${T_A}$ is isothermally expanded to twice its initial volume. It is then compressed at constant pressure to its original volume. Finally, the gas is compressed at constant volume to its original pressure ${P_A}.$ The correct $P-V$ and $P-T$ diagrams indicating the process are

The $VT$ curve for a thermodynamic process is given. Identify the corresponding $PV$ curve.

$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. Which of the following diagrams represents the same process in a $P-T$ graph?

Three samples of the same gas $A, B$ and $C$ $(\gamma = 3/2)$ have initially equal volume. Now the volume of each sample is doubled. The process is adiabatic for $A$,isobaric for $B$,and isothermal for $C$. If the final pressures are equal for all three samples,the ratio of their initial pressures is:

An engine (consisting of one mole of an ideal gas in a cylinder with a piston) follows the cycle shown in the figure. Find the heat exchanged by the engine with the surroundings in each part of the cycle. Given $C_V = \frac{3}{2}R$.
$(a)$ $A$ to $B$: Constant volume
$(b)$ $B$ to $C$: Constant pressure
$(c)$ $C$ to $D$: Adiabatic expansion
$(d)$ $D$ to $A$: Constant pressure

Five moles of an ideal gas has pressure $p_0$,volume $V_0$,and temperature $T_0$. The gas is expanded to volume $3V_0$ along a path such that the pressure $p$ changes as a function of volume $V$ as $p = p_0(V/V_0)$. The pressure is then reduced to $p_0$ while maintaining constant volume. Finally,the gas undergoes an isobaric compression until the volume and temperature return to $V_0$ and $T_0$,respectively. The total work done by the gas during the entire process is: