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 $0 \ ^\circ C$,
$C_p(H_2O, l) = 75.3 \ J \ mol^{-1} \ K^{-1}$,
$C_p(H_2O, s) = 36.8 \ J \ mol^{-1} \ K^{-1}$)

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 $kJ \ mol^{-1}$.

The enthalpy of combustion of carbon monoxide at $17 ^\circ C$ and constant volume is $-283.3 \ kJ$. Calculate the enthalpy of combustion at constant pressure in $kJ$.

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

List-$I$	List-$II$
$A$. Spontaneous process	$I$. $\Delta H < 0$
$B$. Process with $\Delta P = 0; \Delta T = 0$	$II$. $\Delta G_{T, P} < 0$
$C$. $\Delta H_{reaction}$	$III$. Isothermal and isobaric process
$D$. Exothermic process	$IV$. [Bond energies of molecules in reactants] - [Bond energies of product molecules]

Choose the correct answer from the options given below:

Consider the following statements:
Statement-$I$: Both internal energy $(U)$ and work $(w)$ are state functions.
Statement-$II$: During the free expansion of an ideal gas into vacuum,the work done is zero.
The correct answer is:

The reversible expansion of an ideal gas under adiabatic and isothermal conditions is shown in the figure. Which of the following statement$(s)$ is (are) correct?
$(A)$ $T_1 = T_2$
$(B)$ $T_3 > T_1$
$(C)$ $W_{\text{isothermal}} > W_{\text{adiabatic}}$
$(D)$ $\Delta U_{\text{isothermal}} > \Delta U_{\text{adiabatic}}$