Solution 44E

Step 1

The thermal energy per degrees of freedom is given by

So if there are f degrees of freedom per molecule, then the energy per molecule is given by

Now if there are N number of molecule in the gas, then the total thermal energy is given by

From the above equation we can write that

Now, the number of molecule per mole is given by

As stated in the problem, the number of degrees of freedom for the water molecule is

Hence the molar specific heat at constant volume will be for water vapor will be

Now the molar mass of water is

So the specific heat at constant volume of the water vapor is