Helium gas undergoes a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in the figure. The efficiency of this cycle is nearly ....... $\%$ (Assume the gas to be an ideal gas).

Carbon monoxide is taken around the closed cycle $abc$. The process $bc$ is isothermal as shown in the figure. When the temperature of the gas is increased from $300 \ K$ to $1000 \ K$,it absorbs $7000 \ J$ of heat in going from $a$ to $b$. The heat released by the gas during the process $ca$ is ...... $J$.

$A$ reversible cyclic process for an ideal gas is shown below. Here,$P, V$,and $T$ are pressure,volume,and temperature,respectively. The thermodynamic parameters $q, w, H$,and $U$ are heat,work,enthalpy,and internal energy,respectively.
The correct option$(s)$ is (are):
$(A)$ $q_{AC} = \Delta U_{BC}$ and $W_{AB} = P_2(V_2 - V_1)$
$(B)$ $W_{BC} = P_2(V_2 - V_1)$ and $q_{BC} = H_{AC}$
$(C)$ $\Delta H_{CA} < \Delta U_{CA}$ and $q_{AC} = \Delta U_{BC}$
$(D)$ $q_{BC} = \Delta H_{AC}$ and $\Delta H_{CA} > \Delta U_{CA}$

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

If one mole of an ideal gas at $(P_{1}, V_{1})$ is allowed to expand reversibly and isothermally ($A$ to $B$),its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $(B \rightarrow C)$. Then it is restored to its initial state by a reversible adiabatic compression ($C$ to $A$). The net work done by the gas is equal to ...... .

Starting at temperature $300 \; K,$ one mole of an ideal diatomic gas $(\gamma=1.4)$ is first compressed adiabatically from volume $V_{1}$ to $V_{2}=\frac{V_{1}}{16}.$ It is then allowed to expand isobarically to volume $2V_{2}.$ If all the processes are quasi-static,then the final temperature of the gas (in $K$) is (to the nearest integer):