One gram sample of $NH_4NO_3$ is decomposed in a bomb calorimeter. The temperature of the calorimeter increases by $6.12 \ K$. The heat capacity of the system is $1.23 \ kJ/K$. What is the molar heat of decomposition for $NH_4NO_3$ in $kJ/mol$?

$A$ gas at $10 \, atm$ pressure and $300 \, K$ temperature undergoes adiabatic reversible expansion to $5 \, atm$ pressure and $290 \, K$ temperature. The molar heat capacity $C_v$ of the gas in $cal \, mol^{-1} \, K^{-1}$ is:

Assertion : $\Delta H$ and $\Delta E$ are almost same for the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$.
Reason : All reactants and products are gases.

For the reaction at $25^{\circ} C$, $X_2O_{4(l)} \longrightarrow 2 XO_{2(g)}$, $\Delta U$ and $\Delta S$ are $2.1 \ kCal$ and $20 \ cal \ K^{-1}$ respectively. What is $\Delta G$ for the reaction at the same temperature? $(R = 2 \ cal \ K^{-1} \ mol^{-1})$

Consider the following reaction :
$2A (g) + B (g) \rightarrow 2D(g)$
$\Delta U^{\circ} = -10 \text{ kJ mol}^{-1}$ and $\Delta S^{\circ} = -44 \text{ J K}^{-1} \text{ mol}^{-1}$ at $298 \text{ K}$.
Identify the correct option with $\Delta G^{\circ}$ for the reaction and spontaneity of the reaction at $298 \text{ K}$.
(Given : $R = 8.31 \text{ J mol}^{-1} \text{ K}^{-1}$)

Match List-$I$ with List-$II$. Given $V_1$ and $V_2$ are initial and final volumes respectively.

List-$I$ (Isothermal process)	List-$II$ (Expression)
$A$. Reversible expansion	$I$. $q = 0$
$B$. Free expansion	$II$. $q = nRT \ln \frac{V_2}{V_1}$
$C$. Irreversible Compression	$III$. $w = -P_{ext}(V_1 - V_2)$
$D$. Cyclic reversible	$IV$. $\frac{q_{rev}}{T} = 0$