= Adiabatic work in a comoving volume
{title2=$d(\rho c^2V)=-P\,dV$}
For a homogeneous cosmic fluid, the physical volume bounded by fixed <comoving coordinates> obeys $V\propto a^3$. The <cosmological continuity equation> therefore gives $d(\rho c^2V)=-P\,dV$. This is the <first law of thermodynamics> with conserved <entropy> and no additional chemical work. The <internal energy> of that volume need not be constant: a component with negative <pressure> gains <internal energy> as the universe expands. Local <stress-energy conservation> does not imply a global conserved <energy> for an arbitrary expanding spacetime.
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