# Two gases separated by a piston

• GandalfTheGrey
In summary, the question asks about the equilibrium state of two ideal gases separated by a fixed piston that only allows molecules of one gas to pass through. The initial pressures, volumes, temperatures, and number of molecules on each side are given. To solve this, we need to use the ideal gas law, the fact that the partial pressure of gas 1 must be equal on both sides at equilibrium, and the conservation of internal energy. This results in a system of 5 variables and 4 equations. The solution involves an adiabatic reversible expansion and the final number of moles of gas 1 remaining in the right chamber at equilibrium. With this hint, the problem can be solved by using the equation P1fV1^
GandalfTheGrey

## Homework Statement

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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?

## Homework Equations

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

## The Attempt at a Solution

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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?

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.

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

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

GandalfTheGrey said:
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)
Very nice.

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

Chestermiller said:
Have you been able to complete the solution now? If not, I can help further.
I've completed the solution to this problem, but would like to compare notes. Any chance? What about someone else besides the OP?

## What is the purpose of a piston in separating two gases?

The piston is used to create a barrier between two gases in order to prevent them from mixing and to allow for separate measurements or reactions to take place.

## How does a piston separate two gases?

The piston works by creating a physical barrier between the two gases, typically in a closed container. The piston can be moved to adjust the volume of each gas and control the pressure and temperature.

## What factors affect the behavior of two gases separated by a piston?

The behavior of two gases separated by a piston can be affected by factors such as temperature, pressure, volume, and the type of gases involved. These factors can impact the rate of diffusion and the equilibration of the gases.

## Can gases be mixed after being separated by a piston?

Yes, gases can be mixed after being separated by a piston by adjusting the position of the piston or by removing the barrier altogether. This allows for the gases to reach equilibrium and mix together.

## What are some real-world applications of using a piston to separate gases?

A piston can be used to separate gases in various industrial processes, such as in chemical reactions, gas purification, and gas storage. It can also be used in laboratory experiments and in the functioning of engines and compressors.

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