  We make a first principle study of gravitational pressure in cosmic
thermodynamics. The pressure is directly derived from the unified first law, in
fact the Einstein field equation in spherically symmetric spacetime. By using
this pressure, we obtain the thermodynamics for the FRW universe, especially
presenting the gravitational equation of state for the FRW spacetime itself,
i.e. $P=P(R_A, T)$ for the first time. Furthermore, we study the Joule-Thomson
expansion as an application of the thermodynamic equation of state to find the
cooling-heating property of the FRW universe. We demonstrate that there is an
inversion temperature for a FRW universe if its enthalpy ${\cal H}$ is
negative. These investigations shed insights on the evolution of our universe
in view of thermodynamics.
