 Pressure-volume work

The work done by a uniform pressure $P$ on an expanding boundary is $PdV$. With internal energy $U$, the first law of thermodynamics for an adiabatically expanding region reads $dU=-PdV$. For a homogeneous cosmological perfect fluid, $U=\rho V$ and $V\propto a^3$ give the cosmological continuity equation $\dot{\rho }+3H(\rho +P)=0$.