JEE Advanced · 2023 · 04 Jun 2023 · Paper 2 · Chemical Thermodynamics

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given.
${\mathrm{S}}_{\mathrm{T}}$ and ${\mathrm{S}}_0$ are entropies of the phases at temperatures T and 0 K, respectively.

(see diagram)

The transition temperature for $\alpha$ to $\beta$ phase change is 600 K and ${\mathrm{C}}_{\mathrm{P},\beta }-{\mathrm{C}}_{\mathrm{P},\alpha }=1\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$.
Assume $\left({\mathrm{C}}_{\mathrm{P},\beta }-{\mathrm{C}}_{\mathrm{P},\alpha }\right)$ is independent of temperature in the range of 200 to $700\mathrm{K}.{\mathrm{C}}_{\mathrm{P},\alpha }$ and ${\mathrm{C}}_{\mathrm{P},\beta }$ are heat capacities of $\alpha$ and $\beta$ phases, respectively.

The value of entropy change, ${\mathrm{S}}_{\beta }-{\mathrm{S}}_{\alpha }$ (in $\mathrm{J}{\mathrm{mol}}^{-1}{\mathrm{K}}^{-1}$ ), at 300 K is ____.
[Use : $\ln 2=0.69$
Given : ${\mathrm{S}}_{\beta }-{\mathrm{S}}_{\alpha }=0$ at 0 K]