Calculating quality of steam after isentropic expansion

[Ortix]

Homework Statement

Saturated steam with a pressure of 30 bars is isentropically expanded to a pressure of 1 bar. What is the quality (x) of the steam after expansion?

Homework Equations

No clue. I do have a table containing all necessary data such as temperature, specific volume, internal energy, enthalpy and entropy at the afore mention pressure states.

The Attempt at a Solution

No clue where to start.

The problem is that I have no clue where to start. I know that there is no change in entropy, and that I need to calculate the quality. That is done by a simple formula but there are a couple containing either enthalpy, specific volume or specific energy, and all of this is confusing me!

A nudge in the right direction anyone? :D

 

[LawrenceC]

Here is a clue: If it is expanded isentropically, what does that tell you about a property after the expansion?

 

[Ortix]

Here is a clue: If it is expanded isentropically, what does that tell you about a property after the expansion?

entropy remains constant, meaning that there is no heat exchanged with the exterior. All heat is contained within the system. But does that also mean that the temperature stays the same? I actually don't think so. I do know this formula, but this doesn't get me anywhere:

s= (1-x)s2 +xs1

 

[LawrenceC]

That's not where I'm trying to lead you.

You know the state of the steam at the high pressure because it is saturated. It is expanded isentropically so entropy is constant. You know the final pressure and you know the final entropy of the final state. Therefore you can determine the quality.

 

[Ortix]

So you are saying that the entropy of the satured water at both states (1 bar and 30 bar) is constant. In the table it equals sf=2.64 and sg=6.18

the formula is s=sf + x(sg-sf)

what do I put for s then?

 

[LawrenceC]

Initially you have steam at a quality of 100%. That pins down the entropy. After the expansion you have a mixture of liquid water and steam(vapor). If entropy is constant, what do you think you should do?

 

[Ortix]

I think I have to calculate the entropy (s) at 30 bars with x=1. Would that be the correct first step?

 

[LawrenceC]

Look it up in steam tables. But yes, that would be a correct first step.