An ideal monoatomic gas expands to twice its volume. If the process is isothermal,the magnitude of work done by the gas is $W_i$. If the process is adiabatic,the magnitude of work done by the gas is $W_a$. Which of the following is true?

An ideal monoatomic gas is carried around the cycle $ABCDA$ as shown in the figure. The efficiency of the gas cycle is

Thermodynamic processes are indicated in the following diagram. Match the following:

Column-$1$	Column-$2$
$P$: Process-$I$	$A$: Adiabatic
$Q$: Process-$II$	$B$: Isobaric
$R$: Process-$III$	$C$: Isochoric
$S$: Process-$IV$	$D$: Isothermal

One mole of a monoatomic ideal gas goes through a thermodynamic cycle,as shown in the volume versus temperature $(V-T)$ diagram. The correct statement$(s)$ is/are :
[$R$ is the gas constant]
$(1)$ Work done in this thermodynamic cycle $(1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1)$ is $|W| = \frac{1}{2} RT_0$
$(2)$ The ratio of heat transfer during processes $1 \rightarrow 2$ and $2 \rightarrow 3$ is $\left|\frac{Q_{1 \rightarrow 2}}{Q_{2 \rightarrow 3}}\right| = \frac{5}{3}$
$(3)$ The above thermodynamic cycle exhibits only isochoric and adiabatic processes.
$(4)$ The ratio of heat transfer during processes $1 \rightarrow 2$ and $3 \rightarrow 4$ is $\left|\frac{Q_{1 \rightarrow 2}}{Q_{3 \rightarrow 4}}\right| = \frac{1}{2}$

$A$ monoatomic gas at pressure $P$ having volume $V$ expands isothermally to a volume $3V$ and then adiabatically to a volume $81V$. The final pressure of the gas is $(\gamma = 5/3)$.

Two moles of helium gas $\left(\gamma = \frac{5}{3}\right)$ at $27^{\circ} C$ is expanded at constant pressure until its volume is doubled. Then it undergoes an adiabatic change until the temperature returns to its initial value. The work done during the adiabatic process is (universal gas constant $R = 8.3 \ J \ mol^{-1} \ K^{-1}$) (in $J$)