What is the molar heat capacity of water? (R | vedclass

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(A) Water $(H_2O)$ is a non-linear triatomic molecule. According to the equipartition theorem,each atom has $3$ degrees of freedom.For a molecule with

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$9R$

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(A) Water $(H_2O)$ is a non-linear triatomic molecule. According to the equipartition theorem,each atom has $3$ degrees of freedom.For a molecule with $N$ atoms,the total degrees of freedom $f = 3N$.For water,$N = 3$ (one oxygen and two hydrogen atoms),so $f = 3 	imes 3 = 9$.The internal energy $U$ for $1 	ext{ mole}$ of water is given by $U = \frac{f}{2} RT = \frac{9}{2} RT$.However,in the context of specific heat capacity for water in the solid state (ice) or considering vibrational modes,the Dulong-Petit law approximation for a triatomic solid is often used,where each atom contributes $3k_BT$ (kinetic + potential energy).Total energy $U = 3 	imes 3k_BT 	imes N_A = 9RT$.The molar heat capacity $C = \frac{dU}{dT} = 9R$.

What is the molar heat capacity of water? ($R$ is the universal gas constant.)

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