State
what is meant by internal energy,
the basic assumption of the kinetic theory of gases that leads to the conclusion that there is zero potential energy between the molecules of an ideal gas.
The pressure 
and volume 
of an ideal gas are related by
where 
is the number of molecules, 
is the mass of a molecule and 
is the mean-square speed of the molecules. Use this equation to show that the mean kinetic energy 
of a molecule is given by
where 
is the Boltzmann constant and 
is the thermodynamic temperature.
A cylinder contains 
of oxygen gas at a temperature of 
. The mass of 
of oxygen gas is 
. It may be assumed that the oxygen behaves as an ideal gas. Calculate, for the oxygen gas in the cylinder,
the mean kinetic energy of a molecule,
the number of molecules,
the total internal energy.
