# Thermodynamics: piston/cylinder problem

1. Apr 29, 2013

### cdot

1. The problem statement, all variables and given/known data

A piston/cylinder contains 2 kg of water at 20 degrees Celsius with a volume of .1 cubic meters. By mistake,someone locks the piston, preventing it from moving while we heat the water to saturated vapor. Find the final temperature and volume and the process work

2. Relevant equations

I think these are relevant equations?:
specific heat of liquid water is 4.22 kJ/kg*K
specific heat at constant volume is the partial derivative of u (internal energy) with respect to T

3. The attempt at a solution

I'm not sure where to begin. Based on the mass of the water and the value of specific heat I know that the energy required to raise the temperature by 1 kelvin is 8.44. Since the specific heat is the derivative of internal energy I know that if I were to integrate 4.22 with respect to temperature from 293 K to t2 I would get the change in internal energy but t2 is one of the things I don't know

2. Apr 29, 2013

### rude man

Well, the final volume and work done seem pretty obvious - if I'm not missing anything -
As for the temperature, did they give you steam tables or other saturtion information? You have to calcuate your specific volume to use them.

Anyone else? Am I missing something big?

3. Apr 29, 2013

### Staff: Mentor

Are you allowed to use the steam tables to solve this problem? Otherwise, do you have an equation for the saturated vapor pressure as a function of temperature?

4. Apr 29, 2013

### rude man

Glad to see you joined in, Chester! (Right now I don't see how p vs. T helps, but I know you'll show us ... )

5. Apr 29, 2013

### Staff: Mentor

Hey Rude Man. If the final pressure isn't too high, you can solve for the final pressure and temperature by knowing the saturated pressure vs temperature, and applying the ideal gas law under the constraint that the final density is fixed.

6. Apr 29, 2013

### rude man

Ooh, ideal gas law! That woulkd not have occurred to me. Is it really valid at the saturation point? I thought it was only good when you're well into the superheated region.

7. Apr 30, 2013

### Staff: Mentor

Hi Rude man,

Well, it's certainly valid at the saturation point if the temperature is low enough. Consider the saturation vapor pressure of water at 20 C, which is only 17.5 mm Hg. But, as you approach the critical temperature, of course, the ideal gas law is not a good approximation at saturation. In any event, for this problem, one could switch to an appropriate EOS for water if one found that the final pressure and temperature were such that the water vapor could not be regarded as ideal.

Chet

8. Apr 30, 2013

### rude man

Thanks Chet. But I must ask - what is EOS? A better state equation like van der Waals? Or steam table? Sure seems easier to go to the tables or accurate T-v diagram!

9. Apr 30, 2013

### Staff: Mentor

Hey, Rude Man.

EOS = Equation of State

I would always tend to like to use a z-factor plot, particularly in a problem like this where only one state is involved. Of course, as we both told the OP, steam tables would be preferred, but we are not sure whether the OP has been taught about the steam tables yet.

Chet