Two identical samples of a gas are allowed to expand $(i)$ isothermally and $(ii)$ adiabatically. The work done is:

One mole of a monoatomic gas and one mole of a diatomic gas are initially in the same state. Both gases are expanded isothermally and then adiabatically,such that they acquire the same final state. Choose the correct statement.

An ideal gas having pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $3V$ and final pressure $P_I$. The same gas is expanded adiabatically to a volume $3V$, the final pressure being $P_A$. The ratio $P_A/P_I$ is $(C_P/C_V = \gamma)$.

In the following figure,four curves $A, B, C$ and $D$ are shown. The curves are

Which of the following statements is incorrect?

$A$ monoatomic gas performs a work of $\frac{Q}{4}$,where $Q$ is the heat supplied to it. The molar heat capacity of the gas during this transformation will be $xR$,where $R$ is the gas constant. Find the value of $x$.