$A$ monoatomic gas at pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is $\left(\gamma = \frac{5}{3}\right)$.

One mole of a monatomic ideal gas is taken through a cycle $ABCDA$ as shown in the $P-V$ diagram. Column $II$ gives the characteristics involved in the cycle. Match them with each of the processes given in Column $I$.

Column $I$	Column $II$
$(A)$ Process $A \rightarrow B$	$(p)$ Internal energy decreases.
$(B)$ Process $B \rightarrow C$	$(q)$ Internal energy increases.
$(C)$ Process $C \rightarrow D$	$(r)$ Heat is lost.
$(D)$ Process $D \rightarrow A$	$(s)$ Heat is gained.
	$(t)$ Work is done on the gas.

Two identical vessels $A$ and $B$ contain equal amounts of an ideal monoatomic gas. The piston of $A$ is fixed,while the piston of $B$ is free to move. The same amount of heat $\Delta Q$ is absorbed by both $A$ and $B$. If the internal energy of $B$ increases by $100 \, J$,what is the change in the internal energy of $A$ (in $, J$)?

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cycle given in the figure? Where, $1 \rightarrow 2$ is adiabatic.

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q : \Delta U : \Delta W$ is

Two cylinders of equal size are filled with an equal amount of ideal diatomic gas at room temperature. Both cylinders are fitted with pistons. In cylinder $A$,the piston is free to move (isobaric process),while in cylinder $B$,the piston is fixed (isochoric process). When the same amount of heat is supplied to both cylinders,the temperature of the gas in cylinder $A$ rises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B$ (in $;K$)?