$1 \ mol$ of $NH_3$ $(\gamma = 4/3)$ gas at $27 \ ^\circ C$ is expanded under reversible adiabatic conditions to make the volume $8$ times. Calculate the work done in $cal$.

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	$iv$. $W = - nRT \ln \left(\frac{v_f}{v_i}\right)$

What is the difference between $\Delta H$ and $\Delta U$ for the combustion of methane at $25\,^oC$?

The molar heat capacity $(C_p)$ of $CD_2O$ is $10 \, cal \, K^{-1} \, mol^{-1}$ at $1000 \, K$. The change in entropy associated with cooling of $32 \, g$ of $CD_2O$ vapour from $1000 \, K$ to $100 \, K$ at constant pressure will be.....$cal \, deg^{-1}$ ($D = $ deuterium,atomic mass $= 2 \, u$)

For the reaction,$X_2O_{4(l)} \to 2XO_{2(g)}$,$\Delta U = 2.1 \ kcal$ and $\Delta S = 20 \ cal \ K^{-1}$ at $300 \ K$. Calculate $\Delta G$ in $kcal$.

Calculate the work done for the following reaction at $27^{\circ}C$: $C_2H_4(g) + H_2(g) \rightarrow C_2H_6(g)$ $(R = 8.314 \text{ J K}^{-1} \text{mol}^{-1})$ (in $\text{ J}$)