to
during
which the pressure falls from
to
A Level Physics Notes: Thermal Physics and Gases – Isothermal Expansion of an Ideal Gas
An isothermal expansion of a gas is such that the temperature of
the gas is kept constant. The diagram below illustrates the
isothermal expansion of a gas fromtoduring
which the pressure falls fromto
The gas expands during this expansion, so work is done by the gas. The amount of work done is equal to the area under the graph. We can write it as an integral:
If the gas is ideal then we can sue the ideal gas
equation
rearranged
as
to
obtain the integral
We can evaluate this integral quite easily, obtaining
(1)
Because
the
gas does work so W is positive.
Notice also that
for
an isothermal process so that
This
means we can write equation (1) as
