The heat capacity per mole of water is ( $R$ is universal gas constant)\

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Professor PC Thomas Classes · Answer

We treat water like a solid. For each atom average energy is $3 \mathrm{k}_{\mathrm{B}} \mathrm{T}$. Water molecule has three atoms, two hydrogen and one oxygen. The total energy of one mole of water is\ $\mathrm{U}=3 	imes 3 \mathrm{k}_{\mathrm{B}} \mathrm{T} 	imes \mathrm{N}_{\mathrm{A}}=9 \mathrm{RT} \quad\left(\because \mathrm{k}_{\mathrm{B}}=\frac{\mathrm{R}}{\mathrm{N}_{\mathrm{A}}}ight)$\ $	herefore$ Heat capacity per mole of water is\ $\mathrm{C}=\frac{\Delta \mathrm{Q}}{\Delta \mathrm{T}}=\frac{\Delta \mathrm{U}}{\Delta \mathrm{T}}=9 \mathrm{R}$\