$A$ monoatomic gas of pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (ratio of specific heats $\gamma = \frac{5}{3}$)

$A$ Carnot cycle for a gas is represented in the pressure-volume $(P-V)$ diagram shown below. Consider the following statements:
$I.$ The area of $ABCD$ is the work done by the gas.
$II.$ The area of $ABCD$ is the total heat absorbed.
$III.$ The change in internal energy of the cycle is zero.
Which of the following is correct?

$1$ mole of rigid diatomic gas performs a work of $Q/5$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{xR}{8}.$ The value of $x$ is $\ldots \ldots \ldots .$ $[R =$ universal gas constant $]$

Three processes form a thermodynamic cycle as shown on the $P-V$ diagram for an ideal gas. Process $1 \rightarrow 2$ takes place at a constant temperature $(300 \ K)$. Process $2 \rightarrow 3$ takes place at a constant volume. During this process,$40 \ J$ of heat leaves the system. Process $3 \rightarrow 1$ is adiabatic and the temperature $T_3$ is $275 \ K$. The work done by the gas during the process $3 \rightarrow 1$ is ..... $J$.

Consider two containers $A$ and $B$ containing monoatomic gases at the same Pressure $(P)$,Volume $(V)$ and Temperature $(T)$. The gas in $A$ is compressed isothermally to $\frac{1}{8}$ of its original volume while the gas $B$ is compressed adiabatically to $\frac{1}{8}$ of its original volume. The ratio of final pressure of gas in $B$ to that of gas in $A$ is ...........

The initial pressure and volume of a gas are $P$ and $V$ respectively. First, it is expanded isothermally to a volume $4V$ and then compressed adiabatically to a volume $V$. The final pressure of the gas will be (given $\gamma = 3/2$): (in $P$)