The specific heat at constant pressure of a real gas obeying $PV^2=RT$ equation is:

Match the following:

List-$I$	List-$II$
$i)$ Isothermal process	$a)$ $0$
$ii)$ Isobaric process	$b)$ $\frac{1}{\gamma-1}[P_2 V_2 - P_1 V_1]$
$iii)$ Isochoric process	$c)$ $\mu RT \ln(\frac{V_2}{V_1})$
$iv)$ Adiabatic process	$d)$ $P(V_2 - V_1)$

The correct answer is:

If one mole of an ideal gas at $(P_{1}, V_{1})$ is allowed to expand reversibly and isothermally ($A$ to $B$),its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value $(B \rightarrow C)$. Then it is restored to its initial state by a reversible adiabatic compression ($C$ to $A$). The net work done by the gas is equal to ...... .

If $R$ is the universal gas constant,the amount of heat needed to raise the temperature of $2$ moles of an ideal monoatomic gas from $273 \ K$ to $373 \ K$ when no work is done is equal to ...... $R$.

Two containers $A$ and $B$ contain equal volumes of an identical gas at the same pressure and temperature. The gas in container $A$ is compressed to half its original volume isothermally,while the gas in container $B$ is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container $B$ to that of gas in container $A$ is

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of $1000 K$ is $0.4$. It extracts $150 J$ of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance $10$. The hot reservoir of the heat pump is at a temperature of $300 K$. Which of the following statements is/are correct:
$(A)$ Work extracted from the Carnot engine in one cycle is $60 J$.
$(B)$ Temperature of the cold reservoir of the Carnot engine is $600 K$.
$(C)$ Temperature of the cold reservoir of the heat pump is $270 K$.
$(D)$ Heat supplied to the hot reservoir of the heat pump in one cycle is $540 J$.