When $Q_1$ amount of heat is supplied to a monatomic gas, the work done by the gas is $W$. When $Q_2$ amount of heat is supplied to a diatomic gas, the work done by the gas is $2W$. Then $Q_1: Q_2=$

Choose the correct statement for processes $A$ and $B$ shown in the figure.

$List-I$ 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?

In a certain thermodynamical process,the pressure of a gas depends on its volume as $P = kV^{3}$. The work done when the temperature changes from $100^{\circ}C$ to $300^{\circ}C$ will be .......... $nR$,where $n$ denotes the number of moles of a gas.

One mole of a diatomic gas does a work $\frac{Q}{3}$,when the amount of heat supplied is $Q$. In this process,the molar heat capacity of the gas is:

$A$ monoatomic gas of 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 (ratio of specific heats $\gamma = \frac{5}{3}$)