State what is meant by an ideal gas.
A fixed amount of helium gas is sealed in a container. The helium gas has a pressure of 
, and a volume of 
at a temperature of 
. The volume of the container is rapidly decreased to 
. The pressure of the helium gas increases to 
and its temperature increases to 
, as illustrated in the figure below.
The average translational kinetic energy 
of a molecule of an ideal gas is given by
where 
is the Boltzmann constant and 
is the thermodynamic temperature. Calculate the change in the total kinetic energy of the molecules of the helium gas.
