Pressure-volume work
= Pressure-volume work
{title2=$\delta W=P\,dV$}
The <work> done by a uniform <pressure> $P$ on an expanding boundary is $P\,dV$. With <internal energy> $U$, the <first law of thermodynamics> for an adiabatically expanding region reads $dU=-P\,dV$. For a homogeneous cosmological <perfect fluid>, $U=\rho V$ and $V\propto a^3$ give the <cosmological continuity equation> $\dot\rho+3H(\rho+P)=0$.