We investigate the thermodynamics of FRW (Friedmann-Robertson-Walker) universe in the extended phase space. We generalize the unified first law with a cosmological constant $Lambda$ by using the Misner-Sharp energy. We treat the cosmological constant as the thermodynamic pressure of the system, and derive thermodynamic equation of state $P = P(V, T)$ for the FRW universe. To clarify our general result, we present two applications of this thermodynamic equation of state, including Joule-Thomson expansions and efficiency of the Carnot heat engines. These investigations lead to physical insights of the evolution of the universe in view of thermodynamics.
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