Piston (pressure, volume, temperature)

[OsDaJu]

Homework Statement

A piston/cylinder combination contains R-134a at x=1 and 1318.1 kPa. Find the exact phase it is in, the temperature, and specific volume.

1. The piston is then pulled up in an isothermal process until the distance from the bottom of the cylinder is doubled. Construct the final phase in the Tv diagram. Label the lines with their values. Find the final temperature, pressure, specific volume, and quality if defined.

2. Repeat if instead the piston is pushed into the cylinder until it is twice as close to the bottom of it as it was.

Homework Equations

V=Vf +x(Vg-Vf)

The Attempt at a Solution

I found the phase to be saturated vapor, the T=50 c and the specific volume 0.01512 (m^3)/Kg before doing 1.1 and 1.2.

For 1.1 and 1.2 I was thinking about using PV=nRT, id this the right way to approach this problem?

 

[anathema]

Yes, using the ideal gas law, PV = nRT, is a good way to approach these problems. However, since the R-134a is not an ideal gas, you may want to use the more accurate real gas equation, such as the Peng-Robinson equation, to find the final temperature, pressure, and specific volume for parts 1.1 and 1.2. Additionally, for part 1.1, since the process is isothermal, you can use the Clausius-Clapeyron equation to find the final pressure and specific volume, assuming the volume of the cylinder remains constant. For part 1.2, you can use the same approach, but with a different initial volume and using the ideal gas law instead of the Clausius-Clapeyron equation.

 

[kerimek]

I would like to clarify that the use of the ideal gas law, PV=nRT, may not be applicable in this scenario as R-134a is not an ideal gas. It is a refrigerant with properties that deviate from those of an ideal gas, therefore it is important to use the appropriate thermodynamic equations for this specific substance.

To find the exact phase, temperature, and specific volume of the R-134a at x=1 and 1318.1 kPa, we can use the thermodynamic tables for R-134a to determine its properties at those conditions. From the tables, we can see that at 1318.1 kPa, the R-134a is in the saturated vapor phase with a temperature of 50°C and a specific volume of 0.01512 (m^3)/Kg.

For 1.1 and 1.2, instead of using the ideal gas law, we can use the equation V=Vf +x(Vg-Vf) to find the final specific volume after the isothermal process. We can also use the appropriate thermodynamic equations to find the final temperature, pressure, and quality (if defined) after the process.

However, it is important to note that the exact solution will depend on the specific conditions and assumptions of the problem, such as the rate of the isothermal process or the presence of any heat transfer. These factors can affect the final values and should be taken into consideration when solving the problem.