How Does Adiabatic Compression Affect Steam and Water Mixtures?

[zircons]

A compressor adiabatically and reversibly compresses a mixture of saturated water and steam from a pressure 1.02 bar and specific volume of 1.25 m^3/kg to 0.473 m^3/kg.

Calculate the fraction of steam at the compressor entrance, the exit entropy, and the exit pressure.

For the fraction of steam at the entrance, I thought it would be the saturated volume of saturated water and steam/the given volume of 1.25. However, the saturated volume of water and steam at 1.02 bar is higher than the given volume of 1.25. That's impossible. I'm confused; what am I doing wrong?

 

[ajd-brown]

dryness fraction is = (weight of steam) / (weight of steam + weight of water)

its late now so i can't do it, (plus i have an assignment due on wednesday) but either tomorrow or wednesday i will help out some more :)

Anthony

 

[Astronuc]

A compressor adiabatically and reversibly compresses a mixture of saturated water and steam from a pressure 1.02 bar and specific volume of 1.25 m^3/kg to 0.473 m^3/kg.

Calculate the fraction of steam at the compressor entrance, the exit entropy, and the exit pressure.

For the fraction of steam at the entrance, I thought it would be the saturated volume of saturated water and steam/the given volume of 1.25. However, the saturated volume of water and steam at 1.02 bar is higher than the given volume of 1.25. That's impossible. I'm confused; what am I doing wrong?

One may wish to check the specific volume of water and steam for saturated conditions at 1.02 bar. Also, consider the quality of the steam, the mass fraction x that is steam and the fraction (1-x) that is liquid. Then consider the significance of "adiabatically and reversibly" and how that relates to the exit conditions.

 

[Chestermiller]

Isn't the specific volume of liquid water, even at saturation, about 0.001 m³/kg? That doesn't sound higher than 1.25.

 

[zircons]

Thank you for your guidance!

I have now calculated the entrance quality of steam and exit entropy. However, I'm having trouble with the exit pressure. I know the inlet pressure, volume, quality, and entropy. I know the exit volume and entropy. The exit quality of steam and temperature must be higher (right?). I'm at a loss at how to connect it to the exit pressure though.

 

[Chestermiller]

Did you reach the conclusion that the exit entropy is the same as the inlet entropy? Assume a final temperature. Can you look up in the steam tables the entropy of saturated steam, the specific volume of saturated steam, the entropy of saturated liquid water, and the specific volume of saturated liquid water at that temperature? From the final entropy of the mixture, calculate the fraction of saturated steam and saturated water to make good on that final entropy. Then check to see if these fractions are also consistent with the final specific volume of the mixture. If they are not consistent, try another temperature.

Depending on what your steam tables are like, you may be able to find the final state without this trial-and-error approach.

 

[zircons]

Oh man, that's the only solution I could think of, but I was hoping I wouldn't need to do the trial-and-error way. My steam tables will require it, along with interpolation :/ Regardless, thank you for your help!

 

[Chestermiller]

It shouldn't be too bad. Make a graph of the mismatch in overall specific volume as a function of the assumed temperature. After plotting a few points, you will see where the graph is heading, and you will make much better guesses of the temperature. Three or four temperature guesses ought to be enough to get you there.