For a reaction,$X_{2(g)} + Y_{2(g)} \rightleftharpoons 2XY_{(g)}$. If $\Delta G_r^o = 20 \ kJ \ mol^{-1}$ and $\Delta S_r^o = -20 \ J \ K^{-1} \ mol^{-1}$ at $200 \ K$. Calculate $\Delta H_r^o$ at $400 \ K$ (Given $\Delta_r C_P = 20 \ J \ K^{-1} \ mol^{-1}$).

$A$ system consisting of $1 \, mole$ of an ideal gas undergoes a reversible process,$A$ $\rightarrow B$ $\rightarrow C$ $\rightarrow A$ (schematically indicated in the figure below). If the temperature at the starting point $A$ is $300 \, K$ and the work done in the process $B \rightarrow C$ is $1 \, L \, atm$,the heat exchanged in the entire process in $L \, atm$ is $....$

Water vapor is an ideal gas. Calculate the internal energy change $(\Delta U)$ when $1 \, \text{mol}$ of water is vaporized at $1 \, \text{bar}$ pressure and $100 \, ^{\circ}C$. (Given: Molar enthalpy of vaporization of water at $1 \, \text{bar}$ and $373 \, K = 41 \, kJ \, \text{mol}^{-1}$ and $R = 8.3 \, J \, \text{mol}^{-1} \, K^{-1}$)

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.

The heat of combustion $\left(kJ \ mol^{-1}\right)$ is highest for

$A$ mixture of $H_2$ and a sufficient quantity of air at $25\,^{\circ}C$ and $1\ atm$ pressure undergoes complete combustion in a closed rigid adiabatic container,leaving behind $H_2O_{(g)}$ and $N_{2(g)}$. If air is a mixture of $80\% N_2$ and $20\% O_2$ by volume and $C_{P(N_2)}$ and $C_{P(H_2O)g}$ are $7.0$ and $8.0\ cal\ deg^{-1}\ mol^{-1}$ respectively,what will be the maximum temperature attained? (Given that: $(\Delta H^o_f)_{H_2O_{(g)}} = -56.0\ kcal/mol$ and it is independent of temperature)...... $K$