$A$ 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 $x$.

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

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

One mole of an ideal monoatomic gas is heated at a constant pressure of one atmosphere from $0^{\circ}C$ to $100^{\circ}C$. Then the change in the internal energy is

The figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part contains an identical gas at pressure $P_0$. Initially,the temperature of the left and right parts is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep it at rest. Find the value of the external force required when thermal equilibrium is reached. ($A =$ Area of the piston)

$A$ cyclic process $ABCA$ is shown in the $V-T$ diagram. The corresponding process on the $P-V$ diagram is: