$C_{(s)} + O_{2(g)} \rightarrow CO_{2(g)} + 400 \; kJ$
$C_{(s)} + \frac{1}{2} O_{2(g)} \rightarrow CO_{(g)} + 100 \; kJ$
When coal of purity $60 \%$ is allowed to burn in the presence of insufficient oxygen,$60 \%$ of carbon is converted into $CO$ and the remaining is converted into $CO_2$.
The heat generated when $0.6 \; kg$ of coal is burnt is (in $; kJ$)

Identify the correct statements from the following:
$I$. $\Delta_{r} G$ is zero for $A \rightleftharpoons B$ reaction.
$II$. The entropy of pure crystalline solids approaches zero as the temperature approaches absolute zero.
$III$. $\Delta U$ of a reaction can be determined using a bomb calorimeter.

Reversible expansion of an ideal gas under isothermal and adiabatic conditions are as shown in the figure.
$AB \to$ Isothermal expansion
$AC \to$ Adiabatic expansion
Which of the following options is not correct?

$2.2 \, g$ of nitrous oxide $(N_{2}O)$ gas is cooled at a constant pressure of $1 \, atm$ from $310 \, K$ to $270 \, K$ causing the compression of the gas from $217.1 \, mL$ to $167.75 \, mL$. The change in internal energy of the process,$\Delta U$ is $-x \, J$. The value of $x$ is $....$ [nearest integer] (Given: atomic mass of $N = 14 \, g \, mol^{-1}$ and of $O = 16 \, g \, mol^{-1}$. Molar heat capacity of $N_{2}O$ is $100 \, J \, K^{-1} \, mol^{-1}$)

For the reaction $2X_{(g)} + Y_{(g)} \to 2Z_{(g)}$ at $298 \ K$,$\Delta U = -10.5 \ kJ$ and $\Delta S^o = -10.5 \ J/K$. Calculate $\Delta G^o$ for the reaction. Will the reaction be spontaneous or not? Explain.

When $128 \, g$ of oxygen gas is heated from $0 \, ^oC$ to $100 \, ^oC$,the average values of $C_v$ and $C_p$ are $5 \, cal \, mol^{-1} \, K^{-1}$ and $7 \, cal \, mol^{-1} \, K^{-1}$ respectively. Find the values of $\Delta U$ and $\Delta H$.