Water, piston-cylinder problem [Thermodynamics]

In summary: State 2 of the homework problem, but he's having trouble. He finds an online calculator that says the final temperature is 827 or 829 degrees C, but he's not sure if that's correct. He also finds that the pressure in State 2 is constant from this point on. He looks up the ideal gas law and finds that it gives him a reduced pressure of 1.5 bar and a reduced temperature of 827 or 829 degrees C. Then, he goes to the table in Moran et al to find the Z factor. He finds that the Z factor is .85, so the final temperature is close to what the online calculator said.
  • #1
leafjerky
43
7

Homework Statement


Okay, so these are usually pretty easy for me to understand, but this one doesn't make sense.

10 kg of water in a piston cylinder arrangement exists as saturated liquid/vapor at 100 kPa, with a quality of 50%. It is now heated so the volume triples. The mass of the piston is such that a cylinder pressure of 200 kPa will float it. Find the final temperature and the heat transfer in the process.

Homework Equations


v = V/m
v - specific volume
V - volume
m - mass

y = yf +xyfg

The Attempt at a Solution



State 1:[/B]
m1 = m2 = m = 10kg
x1 = .5 ---> 2-phase mixture
P1 = 100 kPa = 1 bar
v1 = .0010432 m3/kg + (.5)(1.694 - .0010432)
v1 = .8475 m3/kg

State 2:
v2 = 3*v1 = 2.5425 m3/kg
P2 = 200 kPa --> pressure is constant from this point on

Solutions I have found online say that the final temp is in the 800's. How is that possible? I went into my steam tables (Fundamentals of Engineering Thermodynamics, Moran) and I couldn't figure out the state. I assume it is a superheated vapour. Is this right? If so, I go to the tables and the temp could probably be interpolated between 1.5 bar and 3 bar, but even then it's not close to 800. I believe the answer is 827 or 829 degrees C. Thanks for any help.
 
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  • #2
What temperature does the ideal gas law give you? (This is a pretty low pressure).
 
  • #3
Thank you! I've always been under the assumption to never use ideal gas for non ideal gases though? This is a first for me. Is there a way to know? Thanks again
 
  • #4
leafjerky said:
Thank you! I've always been under the assumption to never use ideal gas for non ideal gases though? This is a first for me. Is there a way to know? Thanks again
Calculate the reduced pressure and the reduced temperature. Then, see the chart in Moran et al for the Z factor. Or better yet, calculate the pseudo-reduced volume and the reduced pressure and use the Z chart in Moran.

Chet
 

Related to Water, piston-cylinder problem [Thermodynamics]

1. What is the water, piston-cylinder problem in thermodynamics?

The water, piston-cylinder problem in thermodynamics is a commonly used example to demonstrate the principles of thermodynamics. It involves a cylinder with a moveable piston, filled with water and heated by a heat source. The goal is to calculate the change in temperature, pressure, and volume of the water as it undergoes a thermodynamic process.

2. How is the water, piston-cylinder problem solved?

The water, piston-cylinder problem is solved by applying the first and second laws of thermodynamics. The first law, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted. The second law states that the total entropy of a closed system will never decrease over time.

3. What are the assumptions made in the water, piston-cylinder problem?

The water, piston-cylinder problem makes several assumptions, including:

  • The water is an incompressible and ideal substance.
  • The system is closed and no mass is exchanged with the surroundings.
  • The piston is frictionless and does not allow for heat transfer.
  • The heat source is constant and does not vary over time.
  • The process is reversible and adiabatic (no heat transfer).

4. What is the significance of the water, piston-cylinder problem in thermodynamics?

The water, piston-cylinder problem is an important example in thermodynamics because it helps to illustrate the concepts of work, heat, and energy transfer in a closed system. It also demonstrates the relationship between pressure, temperature, and volume in a thermodynamic process.

5. How is the water, piston-cylinder problem applied in real-world situations?

The principles and equations used to solve the water, piston-cylinder problem can be applied in various real-world situations, such as in the design and operation of engines, power plants, and refrigeration systems. It is also used in the analysis of chemical and biological reactions, as well as in the study of weather and climate systems.

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