🧲AP Physics 2
FRQ 1 – Mathematical Routines
Unit 9: Thermodynamics
Practice FRQ 1 of 12
1. A rigid, sealed container of fixed volume holds of an ideal monatomic gas. The gas is initially in thermal equilibrium at temperature and pressure . The container is placed in thermal contact with a large thermal reservoir whose temperature can be changed, as shown in Figure 1. The container walls are thin enough that the gas can exchange energy with the reservoir, but the container volume remains constant.
Figure 1. Rigid sealed container of fixed volume in thermal contact with an adjustable-temperature reservoir (constant-volume heating).
Figure 2. Particle-speed comparison between State 1 (300 K) and State 2 (450 K) at constant volume.
Figure 3. Comparing average force exerted on a container wall at State 1 vs State 2.
A.
i. The reservoir temperature is increased until the gas reaches a new equilibrium temperature . Complete the following tasks in Figures 2 and 3.
• Indicate in Figure 2 whether the typical particle speed at State 2 is greater than, less than, or the same as at State 1 by drawing longer, shorter, or equal-length velocity arrows.
• Indicate in Figure 3 whether the average force exerted by the gas on the container wall at State 2 is greater than, less than, or the same as at State 1 by drawing a longer, shorter, or equal-length arrow in each box.
ii. Assume the gas can be modeled as an ideal monatomic gas. Derive an expression for the change in internal energy in terms of , , and . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
B. Indicate whether the heat transferred to the gas is positive, negative, or zero.
______ Positive
______ Negative
______ Zero
______ Positive
______ Negative
______ Zero
Justify your answer.
Figure 4. Pressure–volume diagram for heating at constant volume V = 0.020 m^3 from State 1 to State 2.
