Thermodynamics: using Peng-Robinson's equation of state

In summary, the conversation is about a question on an assignment about thermodynamics. The question involves finding the temperature and pressure in a tank after 50 minutes using the Peng-Robinson equation, given the initial temperature, pressure, and rate of gas escape. The conversation also mentions the use of two MATLAB functions for the PR equation and the need to derive an equation for the partial derivative of entropy with respect to specific volume. The OP is looking for a method to solve the question and hints are given to help with the solution.
  • #1
H2Odrinker
2
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I'm struggling with a question on an assignment about thermodynamics:

Nitrogen gas, initially at a temperature of 170 K and a pressure of 100 bar, escapes from a thermally isolated tank with a volume of 0.15 m³ at a rate of 10 mol/minute. What will be the temperature and pressure in the tank after 50 minutes? Use the Peng-Robinson equation.

We have 2 MATLAB functions involving the PR equation at our disposal: one for finding the molar volume at a given temperature and pressure, one for finding the pressure at a given temperature and molar volume. I already have the molar volume at the beginning and the end of the process, and I figured that this can be considered an adiabatic expansion.

Any thoughts on how to solve this? I don't need a completely worked out answer, a correct and useful method would be just fine.
 
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  • #2
H2Odrinker said:
I'm struggling with a question on an assignment about thermodynamics:

Nitrogen gas, initially at a temperature of 170 K and a pressure of 100 bar, escapes from a thermally isolated tank with a volume of 0.15 m³ at a rate of 10 mol/minute. What will be the temperature and pressure in the tank after 50 minutes? Use the Peng-Robinson equation.

We have 2 MATLAB functions involving the PR equation at our disposal: one for finding the molar volume at a given temperature and pressure, one for finding the pressure at a given temperature and molar volume. I already have the molar volume at the beginning and the end of the process, and I figured that this can be considered an adiabatic expansion.

Any thoughts on how to solve this? I don't need a completely worked out answer, a correct and useful method would be just fine.
What did you calculate for the initial molar volume and the total number of moles in the tank?

If the expansion is adiabatic and reversible, the molar entropy of the tank contents is constant. You need to start out by deriving an equation for the partial derivative of entropy with respect to specific volume for the PR equation of state.
 
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  • #3
Here's an additional hint. The partial derivative of specific entropy with respect to specific volume is given by:
$$\left(\frac{\partial S}{\partial V}\right)_T=\left(\frac{\partial P}{\partial T}\right)_V$$
 
  • #4
It looks like the OP has disappeared on us. Is there anyone else out there interested in pursuing this?
 

1. What is thermodynamics?

Thermodynamics is a branch of physics that deals with the relationship between heat, energy, and work. It studies how these factors affect and change the physical properties of matter.

2. What is the Peng-Robinson equation of state?

The Peng-Robinson equation of state is a mathematical model used to predict the behavior of gases and liquids at various temperatures and pressures. It is often used in the field of thermodynamics to calculate properties such as volume, pressure, and temperature.

3. How is the Peng-Robinson equation of state used in thermodynamics?

The Peng-Robinson equation of state is used in thermodynamics to calculate the properties of real gases and liquids, which are often more complex than ideal gases. It takes into account factors such as intermolecular interactions and non-ideal behavior to provide more accurate predictions.

4. What are the advantages of using the Peng-Robinson equation of state?

One of the main advantages of using the Peng-Robinson equation of state is its ability to accurately predict the behavior of real gases and liquids. It also takes into account a wide range of temperatures and pressures, making it applicable to many different scenarios in thermodynamics.

5. Are there any limitations to using the Peng-Robinson equation of state?

Like any mathematical model, the Peng-Robinson equation of state has its limitations. It is not suitable for systems with highly polar or highly non-polar molecules, and it may not accurately predict properties at extreme temperatures or pressures. Additionally, it is not always able to account for phase changes such as condensation or vaporization.

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