2070_Thermodynamics1_Soln (1)

2070_Thermodynamics1_Soln (1) - Physics 2070 Homework 9 1....

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Physics 2070 Homework 9 1. 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. In this process, which of the quantities, P, V, n, or T, are held constant and which are allowed to change? Volume and number of moles of gas change during this process— the piston moves to a lower position, decreasing the volume, and the valve is opened, allowing some gas to escape, decreasing amount of gas in the cylinder. The pressure and temperature remain the same during this process—assuming that the piston is at rest at the end of the process, the forces on the piston do not change (the weight of the piston, the force exerted by the air on top of the piston, and the force exerted by the gas below the piston) during this process, so the pressure of the gas inside will still need to counteract the weight of the piston and the weight of the air outside the cylinder. Also, the system remains in thermal equilibrium with its surroundings at all times and there is no indication that there is any temperature change in the surroundings during the process. b. 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? The student is not accounting for changes in temperature and/or the amount of gas in the cylinder. In this case, the temperature remains constant, but the number of moles of gas decreases. This will also affect the pressure of the gas in the cylinder. c. Explain why it is not possible to use the ideal gas law to determine whether the pressure changed in this process. The change in the amount of gas is not known in this case.
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2070_Thermodynamics1_Soln (1) - Physics 2070 Homework 9 1....

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