Physics CAPACITIES OF GASES

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CAPACITIES OF GASES

Monatomic Gases

The molecule of a monatomic gas has only three translational degrees of freedom.

The average energy of a molecule at temperature T is `3/2KT`

The molar specific heat at constant volume is `C_v=(dU)/(dT)=3/2R`

For an ideal gas, `C_p - C_v = R`

where `C_p` is the molar specific heat at constant pressure. Thus,

`C_p=5/2R`

The ratio of specific heats `(C_p)/(C_v)=5/3`

Diatomic Gases

The molar specific heats are then given by

`C_v` (rigid diatomic) `=5/2R`, `C_p=7/2R`

`γ` (rigid diatomic) `=7/5`

If the diatomic molecule is not rigid but has in addition a vibrational mode

`C_v=7/2R`, `C_p=9/2R`

`gamma=9/7`

Polyatomic Gases

`C_v = (3 + f ) R`

`C_p = (4 + f ) R`

`gamma=(4+f)/(3+f)`