GATE 2022 MT – Question 57
Assuming Dulong–Petit for a monoatomic solid, $C_p/C_v$ at 500 K is ______ (three decimal places). Given molar volume $7\times10^{-6}$ m$^3$/mol, isothermal compressibility $8\times10^{-12}$ Pa$^{-1}$, isobaric expansivity $6\times10^{-5}$ K$^{-1}$, and $R=8.314$ J K$^{-1}$ mol$^{-1}$.
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Correct answer: 1.059 to 1.071
Explanation
Dulong–Petit gives $C_v=3R=24.942$ J mol$^{-1}$ K$^{-1}$. The identity $C_p-C_v=TV\alpha^2/\kappa_T$ gives $500(7\times10^{-6})(6\times10^{-5})^2/(8\times10^{-12})=1.575$ J mol$^{-1}$ K$^{-1}$.
Therefore $C_p/C_v=1+1.575/24.942=\boxed{1.063}$.