Using Peng-Robison equation to deterimine fluid lost due to leak

[EvilKermit]

Homework Statement

A container having a volume of 40 L contains one of the following fluids att the given initial conditions. After a leak, the temperature and pressure are remeasured. For each option, determine the kilograms of fluid lost due to the leak, using Peng_robinson equation.

methane T(initial) = 300 K, P(initial) = 100 bar T(final) = 300 K, P(final) = 50 bars

Homework Equations

The Peng robinson equation of state is written as:

Z = [tex]\frac{1}{1-bp}[/tex] - [tex]\frac{a}{bRT}\frac{bp}{1+2bp - b^{2}*p^{2}}[/tex]

The Attempt at a Solution

I know how to solve for a and b. If you find it necessary for me to show you this, i can. But I don't see the purpose. However p, which stands for molar density (n/V), I do not understand. Considering the whole point is to find the amount of moles lost, I can't see how this can be solved unless I know the moles in the tank.

 

[poso]

I do not understand how you can solve anything if in
the initial statement the initial ratio of liquid to gas is not defined.

 

[EvilKermit]

You can just ignore this, there's actually another way for the equation to be rearranged so that you don't need to know the value of molar density.

 

[poso]

I can see a practical reason why my earlier question on the level of fluid in the container was irrelevant. The critical temperature for methane is 190 K and the critical pressure is 45 bar. It would seem that the storing conditions you mentioned at 50 and 100 bar and 300 K define the enclosed methane to be in one uniform supercritical fluid state. A fluid level measurement could thus not be done I think.

Anyway, about the PR equation. I have thought a little bit about applying it to your question of the leak. On the left hand side of the equation Z, the compressibility factor is placed. It is defined as: Z = (pressure*molar volume)/(gasconstant*temperature) Molar volume V is equal to 1/p in the equation you have shown. a and b are gas constants for methane. Since you know gas temerature and pressure you can now solve the initial and final state eqations for the differing values of p. Combining it with the known volume gives you the number of moles for both states, with the leak the difference between the two amounts.

What do you think? I at least found it wonderfull to read and think about a state equation for methane!

 

[DeeNos]

As a scientist, my response would be that the Peng-Robinson equation is a thermodynamic model used to predict the behavior of fluids, specifically their pressure, volume, and temperature relationships. It is not meant to determine the amount of fluid lost due to a leak. To determine the amount of fluid lost, we would need to know the initial and final volumes and pressures, as well as the density of the fluid. The Peng-Robinson equation alone cannot provide this information. Additionally, the equation uses molar density (n/V), which would require knowing the number of moles in the container, which is not given in the problem statement. In this case, it would be more appropriate to use the ideal gas law, PV = nRT, to calculate the amount of fluid lost due to the leak.