Thermodynamic Piston problem.

[seang]

A cylinder contains 1kg of saturated H20 at 30C. This piston has a cross-sectional area of .065m^2, a mass of 40kg, and rests on stops. With the piston in this position, the volume of the H20 is .1m^3. The external atmospheric pressure is 94Kpa and g is 9.75m/s^2. Heat is transferred to the system until the cylinder contains saturated H2O vapor.

1. Sketch the problem on T-v and p-v diagrams.
2. What is the water temperature when the piston just moves off of the stops?

I've been stumped on part 2 for hours. Here's how far I am: The first thing I did was calculate the pressure at which the piston would move up off of the stops. Since at that exact moment the piston won't actually be moving, I can say that Psys*Apiston - Patm*Apiston - m(piston)*g = 0.

Solving, I get Psys = (Patm*Apiston + m(piston)*g)/Apiston. This calculation yields 100KPa.




Help?

 

[OlderDan]

I can't visualize the pistion you are describing. I assume it is completely full of water, but I don't get the geometry. What moves when the water evaporates? What doesn't move? Where are these "stops"

 

[seang]

well here is about the best I can do away from home...

The H20 is in the bottom. The piston is frictionless thus the space between it and the cylinder. Hope that helps a bit.

 

[ccarlos300]

Hey if the H2O is at 100kpa and the piston is free to move with the expansion from saturated liquid to saturated vapor then the pressure is a constant and the temperature during the expansion will be the saturated temp. Due to the fact that the substance will be moving along the isobar in a p-t diagram and along the isotherm in the p-v diagram.

Hope that makes sense and helps

 

[rwisz]

1. Sketching the problem on T-v and p-v diagrams would help visualize the changes happening in the system. The T-v diagram would show the temperature and specific volume of the water as it goes through the process, while the p-v diagram would show the pressure and volume changes.

2. To determine the water temperature when the piston just moves off of the stops, we need to use the ideal gas law and the properties of water to calculate the final pressure and temperature of the system. We can assume that the volume of the cylinder remains constant at 0.1m^3.

Using the ideal gas law, we can write:

Pv = mRT

Where P is the pressure, v is the specific volume, m is the mass, R is the gas constant, and T is the temperature.

Since the water is saturated, we can use the saturated steam table to find the specific volume at 30C, which is 0.00104m^3/kg.

Substituting the given values, we get:

P * 0.00104 = 1kg * 8.314 J/mol*K * (30+273)K

Solving for P, we get P = 100.9KPa.

Now, using the calculated pressure and the known volume, we can find the temperature using the saturated steam table again. At 100.9KPa, the temperature of saturated water vapor is 100.1C.

Therefore, the water temperature when the piston just moves off of the stops is 100.1C.