Initial pressure and volume of a gas are $P$ and $V$ respectively. First,its volume is expanded to $4V$ by an isothermal process,and then its volume is reduced to $V$ by an adiabatic process. Find its final pressure if $\gamma = \frac{3}{2}$.

Consider the following statements:
$A$. Zeroth law of thermodynamics gives the concept of temperature.
$B$. First law of thermodynamics gives the concept of internal energy.
$C$. In isothermal expansion of an ideal gas, $\Delta Q \neq \Delta W$.
$D$. The product of intensive and extensive variables is extensive.
$E$. The ratio of any extensive variable to mass will be an extensive variable.
Choose the correct combination of statements from the options given below:

$List-I$ 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?

$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. Which of the following diagrams represents the same process in a $P-T$ graph?

Read the following statements:
$A.$ When the small temperature difference between a liquid and its surroundings is doubled,the rate of loss of heat of the liquid becomes twice.
$B.$ Two bodies $P$ and $Q$ having equal surface areas are maintained at temperatures $10^{\circ}C$ and $20^{\circ}C$. The thermal radiation emitted in a given time by $P$ and $Q$ are in the ratio $1:1.15$.
$C.$ $A$ Carnot engine working between $100 K$ and $400 K$ has an efficiency of $75\%$.
$D.$ When the small temperature difference between a liquid and its surroundings is quadrupled,the rate of loss of heat of the liquid becomes twice.
Choose the correct answer from the options given below:

$A$ cyclic process $ABCD$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?