. We therefore
want
Because the expansion is reversible, . We therefore
want
To do the integral, we need to write P in terms of 
:
The integral is therefore
Note that we don't know 
and 
. Instead, we know 
and
, but since we are given the relationship between and
P, we can calculate the initial and final molar volumes:
Proceding similarly, we get 
. We now have everything we need to calculate
the value of 
:
This is a tiny amount of energy.
This calculation justifies ignoring the work done on or by solids and
liquids when the pressure is changed by reasonable amounts.