Identify the correct statements from the following.
$I$. At $0 \ K$,the entropy of pure crystalline materials approaches zero.
$II$. Entropy for the process,$H_2O_{(l)} \longrightarrow H_2O_{(g)}$ decreases.
$III$. Gibbs' energy is a state function.

Identify the incorrect statements among the following:
$(a)$ All enthalpies of fusion are positive.
$(b)$ The magnitude of enthalpy change does not depend on the strength of the intermolecular interactions in the substance undergoing phase transformations.
$(c)$ When a chemical reaction is reversed,the value of $\Delta_r H^{\circ}$ is reversed in sign.
$(d)$ The change in enthalpy is dependent on the path between the initial state (reactants) and final state (products).
$(e)$ For most of the ionic compounds,$\Delta_{\text{sol}} H^{\circ}$ is negative.

Which of the following equations are correct?
$(A)$ $H = U + PV$
$(B)$ $G = H - TS$
$(C)$ $U = q + W$

Considering the reaction $C_{(s)} + O_{2(g)} \longrightarrow CO_{2(g)} + 393.5 \ kJ$,the signs of $\Delta H, \Delta S$,and $\Delta G$ respectively are:

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?

Match the List-$I$ with List-$II$

List-$I$ Thermodynamic Process	List-$II$ Magnitude in $kJ$
$A$. Work done in reversible, isothermal expansion of $2 \ mol$ of ideal gas from $2 \ dm^3$ to $20 \ dm^3$ at $300 \ K$.	$I$. $4$
$B$. Work done in irreversible isothermal expansion of $1 \ mol$ ideal gas from $1 \ m^3$ to $3 \ m^3$ at $300 \ K$ against a constant pressure of $3 \ kPa$.	$II$. $11.5$
$C$. Change in internal energy for adiabatic expansion of a $1 \ mol$ ideal gas with change of temperature $= 320 \ K$ and $\overline{C}_V = \frac{3}{2} R$.	$III$. $6$
$D$. Change in enthalpy at constant pressure of $1 \ mole$ ideal gas with change of temperature $= 337 \ K$ and $\overline{C}_P = \frac{5}{2} R$.	$IV$. $7$

Choose the correct answer from the option given below: