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If you change k by a, being a the expansion coefficient in the same equation as before, pv**a = constant, the values of a of the reheated steam are 1.3 for the isentropic expansion and a = 1 for the isenthalpic expansion. However, how do i find the ratio as it is the ratio for the ideal gas that shall be used For this equation of state, specific heat ratio, and isentropic expansion factor are equivalent

I’m sizing some psvs and i have read the article “using the ideal gas cp/cv ratio for rv sizing” in which at the end the author concludes “in no case should the real gas specific heat ratio be used as an estimate of the isentropic expansion coefficient, as this can lead to. Assuming ideal gas the cofficient is set to the ratio between cp and cv I believed that modelling an isoenergetic expansion would give me a less conservative worst case downstream temperature, however i am getting isentropic efficiencies lower than i would expect

Whilst the isentropic efficiency is related to work efficiency due to expansion

= actul work / isentropic work assuming a vessel is perfectly insulated (system is perfectly isolated from surrounding), during depressuring, fluid temperature drops and latent heat in the metal will transfer from metal to fluid. For expansion through a valve, the adiabatic process is isenthalpic For expansion of gas in a cylinder, work is done by the gas Yes, this is an adiabatic process also, but easiest to calculate as isentropic assuming you have the nist tables or other thermodynamic data as mentioned earlier

Hope that clarifies just a little. When sizing for subcritical flow for vapour service according to api520 the isentropic expansion coefficient is needed

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