# Two gases separated by a piston

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1. Aug 2, 2017

### GandalfTheGrey

1. The problem statement, all variables and given/known data

Two ideal gases are contained adiabatically and separated by an insulating, fixed piston that blocks the molecules of gas 2 but allows the molecules of gas 1 through(in both directions). The initial pressures, volumes, temperatures and number of molecules on each side is given. What is the equilibrium state?

2. Relevant equations

I don't think they're explicitly necessary for the question.

3. The attempt at a solution

The volumes remain the same, so we basically have 5 variables: The final pressures, temperatures and the net number of molecules that went through the piston. At equilibrium, the partial pressure of gas 1 must be equal on both sides, that gives 1 equation. The ideal gas law, applied to both sides gives 2 more, and the fact that the whole system's internal energy is constant gives 1 more. So I have 5 variables and only 4 equations. What am I missing?

2. Aug 2, 2017

### Staff: Mentor

The portion of gas 1 that has remained in its chamber at final equilibrium has experienced and adiabatic reversible expansion in driving the other portion of this gas through the piston into the other chamber.

3. Aug 2, 2017

### Staff: Mentor

Now that I've given you the above hint, have you figured out how to solve this problem?

4. Aug 2, 2017

### GandalfTheGrey

I think this means that $$P_{1f}V_1^{\gamma} = P_{1i}(\frac{n_{1rf}}{n_1}V_1)^\gamma$$ Where $P_1$ is the pressure of gas 1 on the right, $V_1$ is the volume of the right chamber, $n_1$ is the total number of moles of gas 1, $n_{1rf}$ is the final number of moles of gas 1 remaining in the right chamber at equilibrium. (I'm assuming that gas 1 starts on the right side and gas 2 on the left side)

5. Aug 3, 2017

Very nice.

6. Aug 3, 2017

### Staff: Mentor

Have you been able to complete the solution now? If not, I can help further.

7. Aug 4, 2017

### Staff: Mentor

I've completed the solution to this problem, but would like to compare notes. Any chance? What about someone else besides the OP?