Specific Heat Capacity
- Monatomic Gases
- Diatomic Gases
- Polyatomic Gases
Specific Heats of Monatomic Gases:
The molecule of a monatomic gas has only three translational degrees of freedom.
Thus, the average energy of a molecule at temperature T is
The total internal energy of a mole of such a gas is
The molar specific heat at constant volume, Cv is
For an ideal gas,
where Cp is the molar specific heat at constant pressure. Thus,
The ratio of specific heats
Specific Heats of Diatomic Gases:
A diatomic molecule treated as a rigid rotator like a dumbbell has 5 degrees of freedom: 3 translational and 2 rotational. Using the law of equipartition of energy, the total internal energy of a mole of such a gas is
The molar specific heats are then given by
If the diatomic molecule is not rigid but has, in addition, a vibration mode
Specific Heats of Polyatomic Gases:
A polyatomic molecule has 3 translational, 3 rotational degrees of freedom and a certain number (f) of vibration modes. According to the law of equipartition of energy, it is easily seen that one mole of such a gas has
