$A$ thermodynamic system undergoes a cyclic process through four stages. The energy values involved during this process are $Q_1 = 600 \ J, Q_2 = -400 \ J, Q_3 = -300 \ J$,and $Q_4 = 200 \ J$. The work values are $W_1 = 300 \ J, W_2 = -200 \ J, W_3 = -150 \ J$,and $W_4$. Find the value of $W_4$ in $J$.

Match List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Isothermal	$(I)$ $\Delta W = 0$
$(B)$ Adiabatic	$(II)$ $\Delta Q = 0$
$(C)$ Isobaric	$(III)$ $\Delta U \neq 0$
$(D)$ Isochoric	$(IV)$ $\Delta U = 0$

Choose the correct answer from the options given below:

$A$ gas is expanded from an initial state to a final state along a path on a $P-V$ diagram. The path consists of $(i)$ an isothermal expansion of work $50 J$,$(ii)$ an adiabatic expansion,and $(iii)$ an isothermal expansion of work $20 J$. If the internal energy of the gas is changed by $-30 J$,then the work done by the gas during the adiabatic expansion is: (in $J$)

$A$ polyatomic gas at pressure $P$,having volume $V$ expands isothermally to a volume $3V$ and then adiabatically to a volume $24V$. The final pressure of the gas is (for a polyatomic gas,assume degrees of freedom $f = 6$,so $\gamma = 4/3$):

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 $.2$)

$A$ thermodynamic cycle of an ideal gas is shown in the figure. Choose the correct option which represents the same cycle.