Question

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

• A. 9 R
• B. $\frac{9}{2}R$
• C. 6 R
• D. 5 R

Answer 1

Answer: (A)

We treat water molecules like a solid. For each atom average energy is $3k_{B}T$. Water molecule has three atoms, two hydrogen and one oxygen. The total energy of one mole of water is
$U=3\times 3k_{B}T\times N_A=9RT$
$\left(\because k_B=\frac{R}{N_A}\right)$
$\therefore$ Heat capacity per mole of water is
$C=\frac{\Delta Q}{\Delta T}=\frac{\Delta U}{\Delta T}=9R$