is
based on a simple picture of a gas as a large number of molecules
which move independently, except for occasional elastic collisions
with each other or with the walls of their container.
A Level Physics Notes: Waves and Oscillations – Speed of Sound in an Ideal Gas
The ideal gas law, expressed in the equationis
based on a simple picture of a gas as a large number of molecules
which move independently, except for occasional elastic collisions
with each other or with the walls of their container.
The ideal gas model predicts that the speed of molecules in a gas
composed of a single type of atom is related via the temperature
and
mass
of
a molecule through
where
k is Boltzmann's constant, while the velocity of sound is given by
where
the
ratios of the specific heat capacities at constant pressure and
volume, which at room temperature depends mostly on the shape of the
molecule.
is
typically between 1.2 and 1.7, you can see that the rms speed of the
molecules is closely related (and slightly larger than) to the speed
of sound.
The speed of sound is proportional to
the square root of the temperature and inversely proportional to the
square root of the mass. The speed increases with temperature because
higher temperatures mean faster moving molecules, but decreases with
mass because the molecules in ideal gases at the same temperature all
have the same kinetic energy (
),
so increasingmeans
decreasing