Question

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

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

Answer 1

Answer: (A)

9R

Answer 2

We treat water like a solid. For each atom average energy is $3k_{B}T.$ Water molecular 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

$C = \frac{\Delta Q}{\Delta T} = \frac{\Delta U}{\Delta T} = 9R$