One mole of a diatomic ideal gas undergoes a process shown in $P-V$ diagram. The total heat given to the gas $(\ln 2 = 0.7)$ is (in $P_0 V_0$)

$A$ container is filled with $20$ moles of an ideal diatomic gas at absolute temperature $T$. When heat is supplied to the gas,the temperature remains constant,but $8$ moles dissociate into atoms. The heat energy given to the gas is ......... (in $R T$)

The amount of work,which can be obtained by supplying $200 \, cal$ of heat,is

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?

Match List-$I$ with List-$II$.

$A$. Isobaric	$I$. $\Delta Q = \Delta W$
$B$. Isochoric	$II$. $\Delta Q = \Delta U$
$C$. Adiabatic	$III$. $\Delta Q = 0$
$D$. Isothermal	$IV$. $\Delta Q = \Delta U + P \Delta V$

$\Delta Q = \text{Heat supplied}$,$\Delta W = \text{Work done by the system}$,$\Delta U = \text{Change in internal energy}$,$P = \text{Pressure of the system}$,$\Delta V = \text{Change in volume of the system}$. Choose the correct answer from the options given below:

Column-$I$ shows graphs of thermodynamic processes, and column-$II$ contains information about various thermodynamic variables. Match column-$I$ with the information in column-$II$.

Column-$I$	Column-$II$
$(A)$ $PV$ vs $V$ (Isothermal expansion)	$(P)$ $W$ > 0
$(B)$ $P$ vs $T$ (Isochoric heating)	$(Q)$ $W$ < 0
$(C)$ $P$ vs $V$ (Isobaric expansion)	$(R)$ $\Delta Q$ > 0
$(D)$ $V$ vs $T$ (Isobaric compression)	$(S)$ $\Delta U$ > 0
	$(T)$ $\Delta U$ < 0