Thermodynamics: using Peng-Robinson's equation of state

[H2Odrinker]

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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.

 

[Chestermiller]

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.

 

[Chestermiller]

Here's an additional hint. The partial derivative of specific entropy with respect to specific volume is given by:
$$\left(\frac{\partial S}{\partial V}\right)_T=\left(\frac{\partial P}{\partial T}\right)_V$$

 

[Chestermiller]

It looks like the OP has disappeared on us. Is there anyone else out there interested in pursuing this?