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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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Practice FRQ 1 of 121/12

1. A sealed cylinder contains a sample of monatomic ideal gas. A frictionless, insulating piston of cross-sectional area Ap=2.00×10−3 m2A_p = 2.00× 10^{-3}\ \text{m}^2Ap​=2.00×10−3 m2 can move vertically without leaking gas. The piston has mass mp=8.00 kgm_p = 8.00\ \text{kg}mp​=8.00 kg, and the external pressure above the piston is constant at Patm=1.00×105 PaP_{\text{atm}} = 1.00× 10^5\ \text{Pa}Patm​=1.00×105 Pa. Initially the gas is in equilibrium at temperature T1=300 KT_1 = 300\ \text{K}T1​=300 K and volume V1=3.00×10−3 m3V_1 = 3.00× 10^{-3}\ \text{m}^3V1​=3.00×10−3 m3, as shown in Figure 1. The gas is then heated slowly so that the piston rises while maintaining mechanical equilibrium with the surroundings.

Figure 1. Sealed cylinder containing monatomic ideal gas under a frictionless, insulating piston in mechanical equilibrium with atmospheric pressure.

Figure 1

Figure 2. Molecular-speed vector representations for two equal-volume gas samples (A and B).

Figure 2

Figure 3. Rigid-container gas: temperature change from T to 2T and the corresponding change in average molecular speed.

Figure 3
A.
i.

Complete the following tasks in Figures 2 and 3.

•

Indicate which gas (A or B) has the higher temperature in Figure 2.

•

Indicate which gas (A or B) would exert the greater pressure if each gas were placed in an identical rigid container with the same number of molecules.

•

In Figure 3, the gas temperature is increased from TTT to 2T2T2T while the gas remains in a rigid container. Indicate how the average molecular speed changes by modifying the arrow lengths to represent the new average molecular speed.

ii.

During the slow heating of the gas in Figure 1, the piston rises and the gas expands at constant pressure. Derive an expression for the number of moles nnn of the gas in terms of V1V_1V1​, T1T_1T1​, PatmP_{\text{atm}}Patm​, mpm_pmp​, ApA_pAp​, and the ideal gas constant RRR. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 4. Cylinder-and-piston system heated by a hot reservoir through a conducting plate (thickness L, area A).

Figure 4
B.

Indicate whether the entropy of the gas is increasing, decreasing, or remaining constant at that instant. The cylinder is now placed in thermal contact with a large reservoir at constant temperature TH=600 KT_H = 600\ \text{K}TH​=600 K by pressing the bottom of the cylinder against a flat aluminum plate, as shown in Figure 4. The plate has thickness L=5.00×10−3 mL = 5.00× 10^{-3}\ \text{m}L=5.00×10−3 m, thermal conductivity k=205 W/(m\cdotpK)k = 205\ \text{W/(m·K)}k=205 W/(m\cdotpK), and contact area with the cylinder of A=2.00×10−3 m2A = 2.00× 10^{-3}\ \text{m}^2A=2.00×10−3 m2. While the gas warms, the piston continues to move so that the gas pressure remains constant. Consider the instant when the gas temperature is T=400 KT = 400\ \text{K}T=400 K.

Assume heat transfer occurs only by conduction through the plate and that the temperature of the plate surface in contact with the gas is equal to the gas temperature at that instant.

Increasing
Decreasing
Remaining constant

Justify your answer.

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Free Response Question Practice

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