Sure. In the vapor, the molecules don't interact significantly. So the heat capacity is the sum of the contributions of the separate molecules. It's a fairly good approximation to treat small molecules at room temperature as rigid rotors. Then for monatomic gases, there are 3 degrees of freedom (3 directions of motion, no rotations), so the equipartition theorem gives a heat capacity of (3/2)kB
per atom, where kB
is Boltzmann's constant, about 1.4 10-23
J/K. For diatomic molecules, there are two rotational modes, giving (5/2)kB
net per molecule. For water, there are 3 rotational modes, giving 3kB
net per molecule. These are all constant volume heat capacities. For onstant pressure heat capacities one must add another kB
You can calculate the number of molecules per unit volume, N/V, in the vapor using the ideal gas law:
T, where p is pressure and T is absolute temperature.
You end up with CV
=pV*alpha/T, where alpha is 3/2 for monatomic gases, 5/2 for diatomic gases, and 3 for non-linear but rigid gas molecules. For any ideal gas Cp
Of course you have to be careful to use consistent units in any calculation like this.
(published on 03/04/07)