Calculating quality of steam after isentropic expansion

In summary, the problem involves expanding saturated steam at 30 bars to a pressure of 1 bar. The steam is isentropically expanded, meaning that the entropy remains constant. Using a formula for calculating quality, the final state of the steam can be determined by finding the entropy at both pressure states and solving for the quality. The first step would be to calculate the entropy at 30 bars with a quality of 100%.
  • #1
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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
 
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  • #2
Here is a clue: If it is expanded isentropically, what does that tell you about a property after the expansion?
 
  • #3
LawrenceC said:
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
 
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  • #4
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.
 
  • #5
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?
 
  • #6
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?
 
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  • #7
I think I have to calculate the entropy (s) at 30 bars with x=1. Would that be the correct first step?
 
  • #8
Look it up in steam tables. But yes, that would be a correct first step.
 
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Related to Calculating quality of steam after isentropic expansion

1. How do you calculate the quality of steam after isentropic expansion?

The quality of steam after isentropic expansion can be calculated by using the steam tables or by using the thermodynamic property calculator. The process involves finding the initial and final pressure and temperature values, and using these values to determine the specific volume and internal energy of the steam. Using the specific volume and internal energy values, the quality of the steam can be calculated using the equation: x = (u-uf)/(ug-uf) where x is the quality, u is the specific internal energy, and uf and ug are the specific internal energy values of saturated liquid and saturated vapor, respectively.

2. What is isentropic expansion?

Isentropic expansion is a thermodynamic process in which a substance expands without any change in its entropy. This means that the substance expands while maintaining its internal energy, temperature, and pressure. Isentropic expansion occurs when the process is reversible and adiabatic, meaning that there is no heat transfer and the process is carried out slowly enough to maintain thermodynamic equilibrium.

3. Can the quality of steam after isentropic expansion be greater than 1?

No, the quality of steam after isentropic expansion cannot be greater than 1. This is because a quality of 1 represents pure saturated vapor, which is the maximum possible quality for steam. If the quality after isentropic expansion is greater than 1, it would mean that the steam has been superheated, which is not possible in an isentropic expansion process.

4. What factors can affect the quality of steam after isentropic expansion?

The quality of steam after isentropic expansion can be affected by the initial pressure and temperature of the steam, as well as the type of fluid being expanded. The type of expansion device used can also impact the quality of the steam, as well as the efficiency of the expansion process. Additionally, any external factors, such as heat loss or friction, can also affect the quality of the steam after isentropic expansion.

5. Why is it important to calculate the quality of steam after isentropic expansion?

Calculating the quality of steam after isentropic expansion is important in understanding the thermodynamic behavior of the substance. It can help engineers and scientists determine the efficiency of a system and make necessary adjustments to improve the process. It is also important in the design and operation of various industrial processes, such as steam turbines and compressors, as the quality of steam can affect the performance and reliability of these systems.

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