Identify the incorrect statements from the following.
$I$. For adiabatic process,$\Delta U = w_{ad}$
$II$. Enthalpy is an intensive property
$III$. For the process,$H_2O_{(l)} \rightarrow H_2O_{(s)}$,the entropy increases

Calculate the difference between heat of combustion of carbon monoxide gas at constant pressure and at constant volume at $27^{\circ} C$ (in $cal$)? $(R = 2 \ cal \ K^{-1} \ mol^{-1})$

At $1 \ atm$ pressure,$\Delta S = 75 \ J/K \cdot mol$ and $\Delta H = 30 \ kJ/mol$. The temperature of the reaction at equilibrium is $....... \ K$.

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 $kcal$.

If the standard enthalpy change $\left(\Delta_{r} H^{\theta}\right)$ for a certain reaction at $298 \ K$ and constant pressure is $-1860 \ kJ \ mol^{-1}$,and the standard entropy change $\left(\Delta_{\text{sys}} S^{\theta}\right)$ of the same reaction is $-550 \ J \ K^{-1} \ mol^{-1}$,which one of the following statements is correct?

The quantity of heat (in $J$) required to raise the temperature of $1.0 \, kg$ of ethanol from $293.45 \, K$ to the boiling point and then change the liquid to vapor at that temperature is closest to
[Given,boiling point of ethanol $351.45 \, K$. Specific heat capacity of liquid ethanol $2.44 \, J \, g^{-1} \, K^{-1}$. Latent heat of vaporisation of ethanol $855 \, J \, g^{-1}$ ]