where
A Level Physics Notes: Thermal Physics and Gases – Heat Capacities of Ideal Gases at Constant Volume
For an ideal gas the internal energy depends only on the
temperaturewhere
is
the number of mols and
is
the Universal Gas Constant,
When the temperature increases by a small amount
the
corresponding change in internal energy is
The specific heat capacity of a substance is defined as
so
for a gas withmols
we see the heat capacity at constant volume is
and
the molar heat capacity at constant volume, labelled
is
In fact the above equation only holds for gases whose particles
are single atoms. It is more accurate to say that the molar hear
capacity for an ideal gas is
per
degree of freedom. This allows us to generalise to gases made up of
molecules of two or more atoms.
For a monotomic gas there are 3 degrees of freedom: up and down, forwards and backwards, left and right.
For a diatomic gas there are two extra, 'vibrational' degrees of
freedom and two extra 'rotational' degrees of freedom, each
contributing an extra
to the molar heat capacity at constant volume. For a diatomic gas,
It must be noted though that the vibrational degrees of freedom
only manifest above certain temperatures. For lower temperatures