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 :

What is the specific heat of a gas in an isothermal process and an adiabatic process?

One mole of an ideal gas $\left( \frac{C_p}{C_v} = \gamma \right)$ is heated according to the law $P = \alpha V$,where $P$ is the pressure of the gas,$V$ is the volume,and $\alpha$ is a constant. What is the molar heat capacity of the gas in this process?

One mole of an ideal gas is taken through a cyclic process with alternating isothermal and adiabatic curves. In the $P-V$ diagram, $AB, CD, EF$ are isothermal curves at absolute temperatures $T_1, T_2,$ and $T_3$ respectively, and $BC, DE,$ and $FA$ are adiabatic curves. If $\frac{V_B}{V_A} = 2$ and $\frac{V_D}{V_C} = 2$, then for the cycle shown in the figure, four statements are made below. (Figure is not drawn to scale)
Statement $1$: Ratio of volumes $\frac{V_E}{V_F} = 4$
Statement $2$: Magnitude of work done in isothermal compression $EF$ is $2RT_3 \ln(2)$
Statement $3$: Ratio of heat supplied to the gas in process $AB$ to heat rejected by the gas in process $EF$ is $\frac{T_1}{T_3}$
Statement $4$: Net work done by the gas in the cycle $ABCDEFA$ is $(T_1 + T_2 - 2T_3) R \ln(2)$
Find the number of correct statements given for the cyclic process followed by the gas.

During the melting of a slab of ice at $273 \, K$ at atmospheric pressure,

For an ideal gas, a cyclic process $ABCA$ is shown in the $P-T$ diagram. Which of the following represents the corresponding $P-V$ plot?