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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, rigid cylindrical container holds n=0.200 moln = 0.200\ \text{mol}n=0.200 mol of an ideal monatomic gas. Initially the gas is in thermal equilibrium at temperature T1=300 KT_1 = 300\ \text{K}T1​=300 K and has pressure P1=1.00×105 PaP_1 = 1.00× 10^5\ \text{Pa}P1​=1.00×105 Pa. The container is fitted with a frictionless piston that can be clamped so the gas volume is fixed, or unclamped so the piston can move and maintain a constant external pressure of 1.00×105 Pa1.00× 10^5\ \text{Pa}1.00×105 Pa, as shown in Figure 1. The gas is brought into thermal contact with a large thermal reservoir at temperature T2=450 KT_2 = 450\ \text{K}T2​=450 K. Assume the piston and cylinder are perfectly insulating except where specified, and the gas remains ideal throughout.

Figure 1. Rigid cylinder with frictionless piston in two operating modes: (a) piston clamped (constant volume) and (b) piston unclamped against a constant external pressure of 1.00×10^5 Pa, with the cylinder wall in thermal contact with a reservoir at 450 K.

Figure 1

Figure 2. P–V diagram with initial state 1 shown; student indicates constant-volume heating path to final state 2.

Figure 2

Figure 3. P–V diagram with initial state 1 shown; student indicates constant-pressure heating path to final state 2.

Figure 3
A.
i.

Complete the following tasks in Figures 2 and 3.

•

In Figure 2, the piston is clamped and the gas is heated from T1T_1T1​ to T2T_2T2​ at constant volume. Indicate the qualitative path on the P–VP\text{–}VP–V diagram and label the final state as point 2.

•

In Figure 3, the piston is unclamped and the gas is heated from T1T_1T1​ to T2T_2T2​ at constant pressure P=1.00×105 PaP = 1.00× 10^5\ \text{Pa}P=1.00×105 Pa. Indicate the qualitative path on the P–VP\text{–}VP–V diagram and label the final state as point 2.

ii.

For the constant-pressure heating process (piston unclamped), derive an expression for the work done by the gas, WWW, in terms of nnn, RRR, T1T_1T1​, and T2T_2T2​. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 4. Conduction through a flat slab separating the gas from a thermal reservoir: slab thickness L, contact area A, hot side at Th (reservoir) and cold side at Tc (gas).

Figure 4
B.

Indicate whether thermal energy is transferred from the reservoir to the gas, from the gas to the reservoir, or neither. The piston is clamped so the volume remains fixed at its initial value V1V_1V1​. The thermal contact between the gas and the reservoir occurs only through a flat slab (Figure 4) with thermal conductivity k=0.80 W m−1 K−1k = 0.80\ \text{W}\,\text{m}^{-1}\,\text{K}^{-1}k=0.80 Wm−1K−1, thickness L=4.0×10−3 mL = 4.0× 10^{-3}\ \text{m}L=4.0×10−3 m, and contact area A=2.5×10−2 m2A = 2.5× 10^{-2}\ \text{m}^2A=2.5×10−2 m2. At a particular instant during the heating, the gas temperature is Tg=330 KT_g = 330\ \text{K}Tg​=330 K while the reservoir remains at T2=450 KT_2 = 450\ \text{K}T2​=450 K.

given_values: ["k = 0.80 W·m^-1·K^-1", "L = 4.0×10^-3 m", "A = 2.5×10^-2 m^2", "T2 = 450 K", "Tg = 330 K"]

From the reservoir to the gas
From the gas to the reservoir
Neither

Justify your answer by calculating the magnitude of the instantaneous rate of energy transfer by conduction through the slab at that instant.

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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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