In an irreversible process taking place at constant $T$ and $P$ and in which only pressure-volume work is being done,the change in Gibbs free energy $(dG)$ and change in entropy $(dS)$ satisfy the criteria:

For the reaction,$2 CO + O_2 \longrightarrow 2 CO_2$; $\Delta H = -560 \ kJ$. Two moles of $CO$ and one mole of $O_2$ are taken in a container of volume $1 \ L$. They completely form two moles of $CO_2$. The gases deviate appreciably from ideal behavior. If the pressure in the vessel changes from $70 \ atm$ to $40 \ atm$,find the magnitude (absolute value) of $\Delta U$ at $500 \ K$. $(1 \ L \ atm = 0.1 \ kJ)$

For a hypothetical reaction $A_{2(g)} + B_{2(g)} \rightleftharpoons 2AB_{(g)}$,at $200 \ K$,$\Delta_r G$ and $\Delta_r S$ are $20 \ kJ \ mol^{-1}$ and $-20 \ J \ K^{-1} \ mol^{-1}$ respectively. If $\Delta_r C_p = 20 \ J \ K^{-1} \ mol^{-1}$,find $\Delta_r H$ at $400 \ K$ in $kJ \ mol^{-1}$.

Standard entropies of $X_2, Y_2$ and $XY_3$ are $60, 40$ and $50 \ J \ K^{-1} \ mol^{-1}$ respectively. For the reaction $\frac{1}{2} X_2 + \frac{3}{2} Y_2 \rightleftharpoons XY_3, \Delta H = -30 \ kJ$,to be at equilibrium,the temperature should be ............. $K$.

The enthalpy change on freezing of $1 \ mol$ of water at $5 \ ^\circ C$ to ice at $-5 \ ^\circ C$ is ..... $kJ \ mol^{-1}$.
(Given $\Delta _{fus}H = 6 \ kJ \ mol^{-1}$ at $0 \ ^\circ C$,
$C_p(H_2O, l) = 75.3 \ J \ mol^{-1} \ K^{-1}$,
$C_p(H_2O, s) = 36.8 \ J \ mol^{-1} \ K^{-1}$)

Which of the following relations are correct?
$(A)$ $\Delta U = q + p \Delta V$
$(B)$ $\Delta G = \Delta H - T \Delta S$
$(C)$ $\Delta S = \frac{q_{rev}}{T}$
$(D)$ $\Delta H = \Delta U - \Delta nRT$
Choose the most appropriate answer from the options given below: