The graph for $y = 1 - e^{-x}$ is represented by (for $x > 0$):

$A$ given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored and its pressure is then found to be $0.75$ of its initial pressure. The ratio of the specific heats of the gas is approximately:

Match List-$I$ with List-$II$ :

List-$I$	List-$II$
$A$. Isothermal Process	$I$. Work done by the gas decreases internal energy
$B$. Adiabatic Process	$II$. No change in internal energy
$C$. Isochoric Process	$III$. The heat absorbed goes partly to increase internal energy and partly to do work
$D$. Isobaric Process	$IV$. No work is done on or by the gas

Choose the correct answer from the options given below :

Two moles of a monoatomic ideal gas is confined in a container and is heated such that its temperature increases by $10\,^{\circ}C$. The approximate change in its internal energy is ..... $J$. $(R = 8.31\, J/mol\cdot K)$

An ideal gas at pressure $P$ and volume $V$ is expanded to volume $2V$. Column $I$ represents the thermodynamic processes used during expansion. Column $II$ represents the work done during these processes in random order:

Column $I$	Column $II$
$(p)$ isobaric	$(x)$ $\frac{PV(1 - 2^{1 - \gamma})}{\gamma - 1}$
$(q)$ isothermal	$(y)$ $PV$
$(r)$ adiabatic	$(z)$ $PV \ln 2$

The correct matching of column $I$ and column $II$ is given by:

For an ideal gas,which of the following statements is correct?