Two gases have the same initial pressure,volume,and temperature. They expand to the same final volume,one adiabatically and the other isothermally.

$A$ gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i = 10^5 \text{ Pa}$ and volume $V_i = 10^{-3} \text{ m}^3$ changes to a final state at $P_f = (1/32) \times 10^5 \text{ Pa}$ and $V_f = 8 \times 10^{-3} \text{ m}^3$ in an adiabatic quasi-static process, such that $P^3 V^5 = \text{constant}$. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at $P_i$, followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately: (in $\text{ J}$)

$A$ monoatomic gas at a pressure $P$,having a volume $V$ expands isothermally to a volume $4V$ and then adiabatically to volume $16V$. The final pressure of the gas is (Take $\gamma = \frac{5}{3}$)

$List-I$ describes thermodynamic processes in four different systems. $List-II$ gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process.

$List-I$	$List-II$
$(I)$ $10^{-3} \, kg$ of water at $100^{\circ} C$ is converted to steam at the same temperature, at a pressure of $10^5 \, Pa$. The volume of the system changes from $10^{-6} \, m^3$ to $10^{-3} \, m^3$. Latent heat of water $= 2250 \, kJ/kg$.	$(P)$ $2 \, kJ$
$(II)$ $0.2 \, moles$ of a rigid diatomic ideal gas with volume $V$ at temperature $500 \, K$ undergoes an isobaric expansion to volume $3V$. Assume $R = 8.0 \, J \, mol^{-1} \, K^{-1}$.	$(Q)$ $7 \, kJ$
$(III)$ One mole of a monatomic ideal gas is compressed adiabatically from volume $V = 1/3 \, m^3$ and pressure $2 \, kPa$ to volume $V/8$.	$(R)$ $4 \, kJ$
$(IV)$ Three moles of a diatomic ideal gas whose molecules can vibrate, is given $9 \, kJ$ of heat and undergoes isobaric expansion.	$(S)$ $5 \, kJ$
	$(T)$ $3 \, kJ$

Which one of the following options is correct?

Two samples $A$ and $B$ of gas are initially at the same pressure and temperature. They are compressed from volume $V$ to $\frac{V}{2}$ ($A$ isothermally and $B$ adiabatically). The relation between the pressure of gas $A$ $(P_A)$ and the pressure of gas $B$ $(P_B)$ is:

$A$ certain amount of gas is taken through a cyclic process $(A-B-C-D-A)$ that has two isobars, one isochore, and one isothermal process. The cycle can be represented on a $P-V$ indicator diagram as: