$A$ 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 (Take $\gamma = 5/3$)

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A) :$ With the increase in the pressure of an ideal gas,the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason $(R) :$ In isothermal process,$PV =$ constant,while in adiabatic process $PV^\gamma =$ constant. Here $\gamma$ is the ratio of specific heats,$P$ is the pressure and $V$ is the volume of the ideal gas. In the light of the above statements,choose the correct answer from the options given below $:$

One mole of a monoatomic ideal gas $\left(c_{V} = \frac{3}{2} R\right)$ undergoes a cycle where it first goes isochorically from the state $\left(\frac{3}{2} P_{0}, V_{0}\right)$ to $\left(P_{0}, V_{0}\right)$,and then is isobarically contracted to the volume $\frac{1}{2} V_{0}$. It is then taken back to the initial state by a path which is a quarter ellipse on the $P-V$ diagram. The efficiency of this cycle is

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300 \ K$. The piston of $A$ 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 $30 \ K$,then the rise in temperature of the gas in $B$ is ..... $K$.

When an ideal gas is heated at constant pressure,what percentage of the heat supplied is used to perform external work? $(\gamma = 5/3)$

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 $\gamma = \frac{C_{P}}{C_{V}}$):