Thermodynamics Compressibility Factor

In summary, the question asks for the molar volume of ethylene at a given temperature and pressure using Corresponding States Theory. This theory involves calculating the reduced temperature and pressure, and using a graph to find the corresponding value of Z. However, the values given do not align with the critical point, making it difficult to determine the molar volume. It is also mentioned that for an ideal gas, Z is constant at a given pressure, but this may not be the case for ethylene at its given conditions.
  • #1
Logan McEntire
4
0

Homework Statement


Please consider ethylene at 152oF and 126 atm. Please determine the molar volume (ft3/lbmole) if Z is determined by Corresponding States Theory.

Homework Equations


Z=PVm/RmT
Vm= Molar volume
R=Rm/M
M= molecular weight
Rm=1545(ft*lbf)/(lbmol*oR)
Zc=(Pcvc)/(R*Tc)
Tc=283 K
Pc=51.2 Bar
M=28.05 Kg/Kmol
PR=P/Pc

The Attempt at a Solution


I can find Vc but that's not 152 oF and 126 atm.
I don't know Z at these conditions either so I can't use the other equation.
 
Physics news on Phys.org
  • #2
What is the reduced temperature and the reduced pressure? Do you have a copy of the graph of z as a function of reduced pressure and reduced temperature?
 
  • #3
I'd imagine that if they say "Z is determined by Corresponding States Theory", that implies it's constant.
 
  • #4
John Park said:
I'd imagine that if they say "Z is determined by Corresponding States Theory", that implies it's constant.
What does this mean? Actually, z is a function of reduced pressure and reduced temperature. Do you know the definition of these quantities?
 
  • #5
For an ideal gas (admittedly a long way from the critical point) z is constant as a function of pressure. Closer to the critical point in general it varies with pressure, but that doesn't seem to rule out the possibility that it takes its critical value here. How would you use the statement about Corresponding States Theory?
 

1. What is the compressibility factor in thermodynamics?

The compressibility factor, also known as the Z factor, is a dimensionless quantity used in thermodynamics to describe the deviation of a gas from ideal gas behavior. It is defined as the ratio of the actual volume of a gas to the volume it would occupy if it behaved like an ideal gas at the same temperature and pressure.

2. How is the compressibility factor calculated?

The compressibility factor can be calculated using the following equation: Z = PV/RT, where P is the pressure, V is the volume, R is the gas constant, and T is the temperature. This equation is based on the ideal gas law and is used to determine the Z factor at a specific pressure and temperature for a given gas.

3. What does a compressibility factor of 1 mean?

A compressibility factor of 1 indicates that the gas behaves like an ideal gas at the given temperature and pressure. This means that the gas molecules do not interact with each other and there are no deviations from ideal gas behavior. A Z factor of 1 is typically seen at low pressures and high temperatures.

4. How does the compressibility factor vary with temperature and pressure?

The compressibility factor is affected by both temperature and pressure. As the temperature increases, the Z factor tends to decrease, meaning the gas becomes more ideal. On the other hand, as pressure increases, the Z factor tends to increase, indicating that the gas deviates more from ideal behavior. This is because at higher pressures, the gas molecules are closer together and interact more, leading to non-ideal behavior.

5. What is the significance of the compressibility factor in thermodynamics?

The compressibility factor is important in thermodynamics because it helps us understand the behavior of real gases and their deviations from ideal gas behavior. It is also used in various equations and calculations, such as the van der Waals equation and the Peng-Robinson equation, to account for these deviations and improve the accuracy of predictions in thermodynamic processes involving gases.

Similar threads

Finding the compressibility factor (Z)
    • Biology and Chemistry Homework Help
Replies
4
Views
33K
Finding vapour pressure using compressibility chart
    • Engineering and Comp Sci Homework Help
Replies
14
Views
4K

Hot Threads

Recent Insights

Back
Top