Calculate the work done in $kJ$ when $3$ moles of an ideal gas at $27^{\circ} C$ expand isothermally and reversibly from $10 \ atm$ to $1 \ atm$ $[R=8.314 \ J \ K^{-1} \ mol^{-1}]$

The difference between $\Delta H$ and $\Delta U$ $(\Delta H - \Delta U),$ when the combustion of one mole of heptane $(l)$ is carried out at a temperature $T$ is equal to (in $,RT$)

Match the following:

List-$I$	List-$II$
$(A) \Delta U = W_{ad}$	$I.$ Isothermal reversible expansion
$(B) \Delta U = q - W$	$II.$ Wall is adiabatic
$(C) \Delta U = -q$	$III.$ Thermally conducting walls
$(D) \Delta U = 0$	$IV.$ Isolated system
	$V.$ Closed system

The correct answer is

State $1 \longleftarrow$ State $2 \longleftarrow$ State $3$
$\left(\begin{array}{c} T=300 \ K \\ P=15 \ bar \\ 1 \ mole \end{array}\right) \left(\begin{array}{c} T=300 \ K \\ P=10 \ bar \\ 1 \ mole \end{array}\right) \left(\begin{array}{c} T=300 \ K \\ P=5 \ bar \\ 1 \ mole \end{array}\right)$
The above shows a cyclic process. Calculate the total work done during one complete cycle. (Assume a single step to reach the next state).

Match List-$I$ with List-$II$.

List-$I$ $(\text{Partial Derivatives})$	List-$II$ $(\text{Thermodynamic Quantity})$
$(A). \left(\frac{\partial G}{\partial T}\right)_{P}$	$(I). C_P$
$(B). \left(\frac{\partial H}{\partial T}\right)_{P}$	$(II). -S$
$(C). \left(\frac{\partial G}{\partial P}\right)_{T}$	$(III). C_V$
$(D). \left(\frac{\partial U}{\partial T}\right)_{V}$	$(IV). V$

Choose the correct answer from the options given below:

$20.0 \ dm^{3}$ of an ideal gas '$X$' at $600 \ K$ and $0.5 \ MPa$ undergoes isothermal reversible expansion until the pressure of the gas is $0.2 \ MPa$. Which of the following options is correct? (Given: $\log\,2=0.3010$ and $\log\,5=0.6989$)