$A$ gas of mass '$m$' and molecular weight '$M$' is flowing in an insulated tube with a velocity '$2V$'. If the flow of the gas is suddenly stopped and all the kinetic energy is utilized to compress the gas,the increase in the temperature of the gas is ($\gamma$ is the ratio of specific heats,$R$ is the universal gas constant).

$A$ 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?

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 ..... $K$.

The ratio of the slopes of isothermal and adiabatic curves is

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(a)$ Isothermal	$(i)$ Pressure constant
$(b)$ Isochoric	$(ii)$ Temperature constant
$(c)$ Adiabatic	$(iii)$ Volume constant
$(d)$ Isobaric	$(iv)$ Heat content is constant

Choose the correct answer from the options given below:

Consider the following volume-temperature $(V-T)$ diagram for the expansion of $5$ moles of an ideal monoatomic gas. Considering only $P-V$ work is involved,the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \rightarrow Y \rightarrow Z$ is $\qquad$ [Use the given data: Molar heat capacity of the gas for the given temperature range,$C_{v,m} = 12 \ J \ K^{-1} \ mol^{-1}$ and gas constant,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$]