An ideal gas follows a process $PT = \text{constant}$. The correct graph between pressure $P$ and volume $V$ is:

One mole of an ideal monoatomic gas undergoes the process $A \rightarrow B \rightarrow C \rightarrow D \rightarrow A$ as shown in the graph. The work done during the process is

Select the correct statement for work, heat, and change in internal energy.

Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal diatomic gas at temperature $T$ $K$. The piston of cylinder $A$ is free to move,while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $dT_{A}$,then the rise in temperature of the gas in cylinder $B$ is (where $\gamma = \frac{C_{P}}{C_{V}}$):

Heat energy of $735\,J$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but does not oscillate. The increase in the internal energy of the gas will be $..........\,J$

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