$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)

The initial pressure and volume of a gas are $P$ and $V$ respectively. First, it is expanded isothermally to a volume $4V$ and then compressed adiabatically to a volume $V$. The final pressure of the gas will be (given $\gamma = 3/2$): (in $P$)

$A$ given amount of gas has an initial state $(P_i, V_i, T_i)$. It expands until its volume becomes $V_f$. Consider the following two cases:
$(a)$ The expansion occurs at constant temperature (isothermal).
$(b)$ The expansion occurs at constant pressure (isobaric).
Draw the $P-V$ diagram for each case. In which of the two cases is the work done by the gas greater?

Two cylinders $A$ and $B$ fitted with pistons contain equal amount of an ideal diatomic gas at $303 \text{ K}$. The piston of cylinder $A$ is free to move and that of cylinder $B$ 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 cylinder $B$ is $63 \text{ K}$, then the rise in temperature of the gas in $A$ is: (in $\text{ K}$)

The ratio of the slopes of isothermal and adiabatic curves is

Starting with the same initial conditions,an ideal gas expands from volume $V_{i}$ to $V_{f}$ in three different ways. The work done by the gas is $W_{1}$ if the process is purely isothermal,$W_{2}$ if the process is purely adiabatic,and $W_{3}$ if the process is purely isobaric. Then,choose the correct option.