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A cylinder with a valve at the bottom is filled with an ideal gas. The valve is now opened and some of the gas escapes slowly. The valve is then closed, after which the piston is observed to be at a lower position. Assume that the system is in thermal equilibrium with the surroundings at all times.

a) Is the final pressure of the gas in the cylinder greater than, less than, or equal to the initial pressure? Explain.

Explain how your answer is consistent with the forces acting on the piston in the initial and final states.

b) In this process, which of the quantities P, V, n, and T are held constant and which are allowed to change?

c) Consider the following incorrect student statement.

"In the ideal gas law, P=nRT/V, so the pressure is inversely proportional to the volume. If you decrease the volume, the pressure has to go up."

What is the flaw in the student's reasoning?

d) Explain why it is not possible to use the ideal gas law to determine whether the pressure changed in this process.

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