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🧲AP Physics 2
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🧲AP Physics 2

FRQ 1 – Mathematical Routines
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Unit 9: Thermodynamics
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FRQ Types & Units

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 1 of 121/12

1. A rigid, sealed container holds n=0.500 moln = 0.500\ \text{mol}n=0.500 mol of an ideal monatomic gas. The gas is initially in equilibrium at pressure P1=1.20×105 PaP_1 = 1.20× 10^5\ \text{Pa}P1​=1.20×105 Pa and volume V1=6.00×10−3 m3V_1 = 6.00× 10^{-3}\ \text{m}^3V1​=6.00×10−3 m3. The gas is taken through a two-step process from state 1 to state 3. In step 1, the gas is heated at constant volume from state 1 to state 2 until the pressure becomes P2=2.40×105 PaP_2 = 2.40× 10^5\ \text{Pa}P2​=2.40×105 Pa. In step 2, the gas expands isothermally from state 2 to state 3 until the pressure becomes P3=1.20×105 PaP_3 = 1.20× 10^5\ \text{Pa}P3​=1.20×105 Pa. A pressure-volume diagram for the process is shown in Figure 1.

Figure 1. Pressure–volume diagram for a two-step process: constant-volume heating from state 1 to state 2, followed by isothermal expansion from state 2 to state 3.

Figure 1

Figure 2. Microscopic model used to compare average molecular speed at state 1 and state 2 (constant volume).

Figure 2

Figure 3. Microscopic collision model used to compare pressure (force per unit area) at state 1 and state 2.

Figure 3
A.
i.

Complete the following tasks in Figures 2 and 3.

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Indicate in Figure 2 whether the average molecular speed of the gas particles in state 2 is greater than, less than, or equal to the average molecular speed in state 1.

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Indicate in Figure 3 whether the average force per unit area exerted on the container walls in state 2 is greater than, less than, or equal to that in state 1.

ii.

For the ideal monatomic gas, derive an expression for the total change in internal energy ΔU1→3\Delta U_{1\to3}ΔU1→3​ in terms of nnn, RRR, and the temperatures T1T_1T1​ and T2T_2T2​. Then determine whether ΔU1→3\Delta U_{1\to3}ΔU1→3​ is positive, negative, or zero for the process shown.

Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 4. Rigid gas container thermally connected to a large reservoir through a conducting slab (conduction only).

Figure 4
B.

Calculate the magnitude of the rate of energy transfer by conduction through the slab at that instant. Then calculate the time required to raise the temperature of the gas from 300 K300\ \text{K}300 K to 600 K600\ \text{K}600 K if the conduction rate remains constant at the value you calculated and all transferred energy goes into increasing the internal energy of the gas. Finally, calculate the entropy change ΔSgas\Delta S_{\text{gas}}ΔSgas​ of the gas for heating from 300 K300\ \text{K}300 K to 600 K600\ \text{K}600 K at constant volume. The container is now brought into thermal contact with a large reservoir at constant temperature TR=600 KT_R = 600\ \text{K}TR​=600 K through a flat slab of material of thickness L=2.0×10−3 mL = 2.0× 10^{-3}\ \text{m}L=2.0×10−3 m and cross-sectional area A=1.5×10−2 m2A = 1.5× 10^{-2}\ \text{m}^2A=1.5×10−2 m2, as shown in Figure 4. The slab has thermal conductivity k=0.20 W/(m\cdotpK)k = 0.20\ \text{W/(m·K)}k=0.20 W/(m\cdotpK). At some instant, the gas temperature is Tgas=300 KT_{\text{gas}} = 300\ \text{K}Tgas​=300 K. Assume the reservoir remains at TRT_RTR​ and that energy is transferred only by conduction through the slab.

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Free Response Question Practice

This practice environment simulates the AP AP Physics 2 Free Response Questions section. Here are some guidelines:

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