At $27 \, ^oC$,one mole of an ideal gas is compressed isothermally and reversibly from a pressure of $2 \ atm$ to $10 \ atm$. The values of $\Delta E$ and $q$ are $(R = 2 \ cal \ K^{-1} \ mol^{-1})$:

Match the following:

$A$. Isothermal process	$i$. $q = \Delta U$
$B$. Adiabatic process	$ii$. $W = - P \times \Delta V$
$C$. Isobaric process	$iii$. $W = \Delta U$
$D$. Isochoric process	$iv$. $W = - nRT \ln \left(\frac{v_f}{v_i}\right)$

$A$ sample of gas is compressed from an initial volume of $2V_0$ to $V_0$ using three different processes.
First: Using reversible isothermal.
Second: Using reversible adiabatic.
Third: Using irreversible adiabatic under a constant external pressure.
Then

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

List-$I$	List-$II$
$A$. Spontaneous process	$I$. $\Delta H < 0$
$B$. Process with $\Delta P = 0; \Delta T = 0$	$II$. $\Delta G_{T, P} < 0$
$C$. $\Delta H_{reaction}$	$III$. Isothermal and isobaric process
$D$. Exothermic process	$IV$. [Bond energies of molecules in reactants] - [Bond energies of product molecules]

Choose the correct answer from the options given below:

Assuming the water vapour to be a perfect gas,calculate the internal energy change when $1 \ mol$ of water at $100^{\circ} C$ and $1 \ bar$ pressure is converted to ice at $0^{\circ} C$. Given the enthalpy of fusion of ice is $6.00 \ kJ \ mol^{-1}$ and heat capacity of water is $4.2 \ J \ g^{-1} {\circ} C^{-1}$.

For the reaction
$A_{(\ell)} \rightarrow 2 B_{(g)}$
$\Delta U = 2.1 \; kcal, \Delta S = 20 \; cal \; K^{-1} \; mol^{-1}$ at $300 \; K$
Hence $\Delta G$ in $kcal \; mol^{-1}$ is