That is, the work done during an adiabatic expansion of a perfect gas is proportional
to the temperature difference between the initial and final states. That is exactly what
we expect on molecular grounds, because the mean kinetic energy is proportional to
T, so a change in internal energy arising from temperature alone is also expected to be
proportional to ΔT. In Further information 2.1 we show that the initial and final temperatures
of a perfect gas that undergoes reversible adiabatic expansion (reversible
expansion in a thermally insulated container) can be calculated from