# Adiabatic expansion of steam through a valve

I'm working on a homework problem, and I have a suspicion the textbook is trying to trick me.

The question is:

"Steam at 20 bar and 300 C is to be continuously expanded to 1 bar. Compute the entropy generated and the work obtained per kilogram of steam if this expansion is done by passing the steam through an adiabatic expansion valve."

My energy and entropy balances give:

$$\dot{W} = \dot{M}(\hat{H}_2 - \hat{H}_1)$$

$$\dot{S}_{gen} = \dot{M}(\hat{S}_2 - \hat{S}_1)$$

where

$$\dot{W} = \dot{W}_s - P\frac{dV}{dt}$$

... but, there is no $\dot{W}_s$ since it's an expansion valve, right? If it was a turbine (which the next question asks), then there would be shaft work, but unless I'm mistaken, there is no shaft work for an expansion valve, right?

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## 1 Answer

Yes. Expansion valve has no work. So you have the final enthalpy (same as initial enthalpy) and pressure. That will give you $S_2$ from the steam tables :).

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Thanks!  Just what I thought. – Nick Feb 21 at 23:10
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