Two moles of an ideal gas undergo free expansion from 10 L to 100 L at 300 K . The values of $\Delta \mathrm{S}_{\text {system }}$ and $\Delta \mathrm{S}_{\text {surroundings }}$ are

( $R$ is universal gas constant)

$$ \text { Consider the reversible processes for } 1.0 \mathrm{~mol} \text { of an ideal gas as shown in the figure. } $$

$w_1, w_2, w_3$ and $w_4$ represent work done (in calories) in the processes $1,2,3$ and 4 , respectively; $\Delta U_2$ and $\Delta U_4$ are changes in the internal energy for the processes 2 and 4, respectively.

[use $\mathrm{R}=2 \mathrm{cal} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ ]

The correct option is

A protein undergoes reversible thermal denaturation from its initial state $\mathbf{N}$ to denatured state $\mathbf{D}$ according to $\mathbf{N} \rightleftharpoons \mathbf{D}$. At $60^{\circ} \mathrm{C}$, the concentrations of both $\mathbf{N}$ and $\mathbf{D}$ are equal at equilibrium, and the standard enthalpy change of denaturation is $666 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The standard entropy change $\Delta \mathrm{S}^{\circ}$ in $\mathrm{kJ} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ ) of the protein upon denaturation at $60^{\circ} \mathrm{C}$ is closest to

Consider the following reaction :

$$ \begin{aligned} & 2 \mathrm{~A}(\mathrm{~g})+\mathrm{B}(\mathrm{~g}) \rightarrow 2 \mathrm{D}(\mathrm{~g}) \\ & \Delta \mathrm{U}^{\ominus}=-10 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { and } \Delta \mathrm{S}^{\ominus}=-44 \mathrm{JK}^{-1} \text { at } 298 \mathrm{~K} . \end{aligned} $$

Identify the correct option with $\Delta \mathrm{G}^{\ominus}$ for the reaction and spontaneity of the reaction at 298 K .

(Given : $\mathrm{R}=8.31 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )