Thermodynamics

The entropy versus temperature plot for phases $\alpha$ and $\beta$ at 1 bar pressure is given. $S_{\mathrm{T}}$ and $S_0$ are entropies of the phases at temperatures $\mathrm{T}$ and $0 \mathrm{~K}$, respectively.




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

\(\text { The value of enthalpy change, } \mathrm{H}_\beta-\mathrm{H}_\alpha \text { (in } \mathrm{J} \mathrm{mol}^{-1} \text { ), at } 300 \mathrm{~K} \text { is }\) ________.