$A$ monoatomic gas at a pressure $P$,having a volume $V$ expands isothermally to a volume $4V$ and then adiabatically to volume $16V$. The final pressure of the gas is (Take $\gamma = \frac{5}{3}$)

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).

If one mole of an ideal gas goes through the process $A \rightarrow B$ and $B \rightarrow C$ as shown in the $P-V$ diagram. Given that $T_A = 400 \, K$ and $T_C = 400 \, K$. If $\frac{P_B}{P_A} = \frac{1}{5}$,then find the total heat supplied to the gas (in $J$). (in $.2$)

What are the limitations of the first law of thermodynamics?

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

For the given $P-V$ diagram of a thermodynamic system,match the curves with their respective thermodynamic processes. ($P$ = Pressure and $V$ = Volume)

Curve	Process
$I$	$a)$ Adiabatic
$II$	$b)$ Isobaric
$III$	$c)$ Isochoric
$IV$	$d)$ Isothermal