🧲AP Physics 2
1. A sealed cylinder contains of a monatomic ideal gas and is fitted with a frictionless, movable piston of cross-sectional area . The cylinder is initially in thermal equilibrium with a large reservoir at temperature . The gas is initially at pressure and volume . A schematic of the apparatus is shown in Figure 1.
Figure 1. Sealed cylinder with movable frictionless piston in thermal contact with an adjustable-temperature reservoir (initial state at T₀ and P₀).
Figure 2. Microscopic model of gas particles at state 0 (T₀) and state 1 (T₁) for comparing average speed and momentum transfer rate at the same volume.
Figure 3. Blank P–V diagram with states 0 and 1 at the same pressure P₀; students sketch the constant-pressure path from 0 to 1.
The reservoir temperature is increased so that the gas reaches a new equilibrium temperature while the piston is free to move.
Complete the following tasks in Figure 2.
Indicate in Panel (b) whether the average speed of the particles is greater than, less than, or equal to that in Panel (a).
Indicate in Panel (b) whether the average rate of momentum transfer to the cylinder wall (and thus the pressure) is greater than, less than, or equal to that in Panel (a) at the same volume.
The gas is heated from to in a quasistatic process at constant pressure . Using Figure 3, sketch the process path from state 0 to state 1.
Derive an expression for the final volume in terms of , , and . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
Figure 4. Heat transfer through a metal plate of thickness L between a hot reservoir and the gas; plate area equals the cylinder cross-sectional area.
Indicate whether the change in entropy of the gas is positive, negative, or zero. The gas undergoes the constant-pressure process from state 0 to state 1, where the final temperature is and the pressure remains . The amount of gas is , and the gas is monatomic and ideal. Assume the process is quasistatic and that no phase changes occur. The heat transfer mechanism is shown in Figure 4.
Positive
Negative
Zero
Justify your answer.
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