The slopes of isothermal and adiabatic curves are related as

$A$ monatomic gas of volume $V$ and pressure $P$ expands isothermally to a volume $27 V$ and then is compressed adiabatically to a volume $V$. The final pressure of the gas is: (in $P$)

In the following figure,four curves $A, B, C$ and $D$ are shown. The curves are

$A$ cyclic process $ABCD$ is shown in the $p-V$ diagram. Which of the following curves represents the same process if $BC$ and $DA$ are isothermal processes?

Three moles of an ideal gas undergo a cyclic process $ABCA$ as shown in the figure. The pressure, volume, and absolute temperature at points $A, B,$ and $C$ are respectively $(P_1, V_1, T_1)$, $(P_2, 3V_1, T_1)$, and $(P_2, V_1, T_2)$. Then the total work done in the cycle $ABCA$ is (where $R$ is the universal gas constant).

$n$ moles of a perfect gas undergo a cyclic process $ABCA$ (see figure) consisting of the following processes:
$A \rightarrow B :$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V_{1}$ to $V_{2}=2V_{1}$ and pressure changes from $P_{1}$ to $P_{2}$.
$B \rightarrow C :$ Isobaric compression at pressure $P_{2}$ to initial volume $V_{1}$.
$C \rightarrow A :$ Isochoric change leading to a change of pressure from $P_{2}$ to $P_{1}$.
Total work done in the complete cycle $ABCA$ is