What I don’t understand is as follows: If you have a pressure of 800 kPa
upstream of the PRV and it gets reduced to 400 kPA, why is the
downstream steam not superheated? The steam downstream is merely
saturated at 4 bar. Where does the extra energy go? Please site sources.
The “Extra Energy” goes into the work required to expand the gas.
The First Law of Thermodynamics essentially states:

U = Q + Ws

(Internal energy) = (Energy Applied as Heat) + (Work the System has done on it)
For PV work, dWs = -Pe*dV

(Differential Change in work) = (The Negative pressure the Gas is
expanding against) times (The Differential Change in Volume the Gas
undergoes).
Where this work term comes from: “On a molecular scale, the nergy
transfer by PV work can be understood in terms of momentum transfer of
the molecules in the system when they bounce off the moving boundary”.
(Koretsky)
If your Steam PRV is insulated and not heated, Q = 0

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