An insulating cylinder contains $4 \text{ moles}$ of an ideal diatomic gas. When a heat $Q$ is supplied to it, $2 \text{ moles}$ of the gas molecules dissociate. If the temperature of the gas remains constant, then the value of $Q$ is ($R$ - universal gas constant).

In thermodynamics,heat and work are

Two moles of a triatomic gas $\left(\gamma = \frac{4}{3}\right)$ at temperature $327^{\circ} C$ expands adiabatically such that its volume becomes $8$ times its initial volume. Later, the temperature of the gas is doubled in an isochoric process. The total work done in the two processes is ($R$ - universal gas constant). (in $R$)

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

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4 V_1$. After this,the gas expands adiabatically and its volume becomes $32 V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{\text{iso}}$ and $W_{\text{adia}}$,respectively. If the ratio $\frac{W_{\text{iso}}}{W_{\text{adia}}} = f \ln 2$,then $f$ is:

Column $I$ contains a list of processes involving the expansion of an ideal gas. Match this with Column $II$ describing the thermodynamic change during this process.

Column $I$	Column $II$
$(A)$ An insulated container has two chambers separated by a valve. Chamber $I$ contains an ideal gas and Chamber $II$ has a vacuum. The valve is opened.	$(p)$ The temperature of the gas decreases
$(B)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $P \propto V^{-2}$	$(q)$ The temperature of the gas increases or remains constant
$(C)$ An ideal monoatomic gas expands to twice its original volume such that its pressure $P \propto V^{-4/3}$	$(r)$ The gas loses heat
$(D)$ An ideal monoatomic gas expands such that its pressure $P$ and volume $V$ follow the behavior shown in the graph	$(s)$ The gas gains heat