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🧲AP Physics 2
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🧲AP Physics 2

FRQ 2 – Translation Between Representations
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Unit 9: Thermodynamics
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Practice FRQ 1 of 161/16

2. A sample of a monatomic ideal gas is sealed in a vertical cylinder by a movable piston of mass M=4.00 kgM = 4.00\ \text{kg}M=4.00 kg and area A=2.50×10−3 m2A = 2.50× 10^{-3}\ \text{m}^2A=2.50×10−3 m2, as shown in Figure 1. The piston moves with negligible friction. The pressure of the air above the piston is Patm=1.01×105 PaP_{\text{atm}} = 1.01× 10^5\ \text{Pa}Patm​=1.01×105 Pa. The cylinder walls and piston are thermally insulating. A solid copper plate of thickness L=2.00×10−2 mL = 2.00× 10^{-2}\ \text{m}L=2.00×10−2 m and cross-sectional area equal to the piston area is placed in firm contact with the bottom of the gas. The bottom surface of the copper plate is in contact with a large water reservoir at constant temperature T0=300 KT_0 = 300\ \text{K}T0​=300 K. The copper has thermal conductivity k=400 W m−1 K−1k = 400\ \text{W}\,\text{m}^{-1}\,\text{K}^{-1}k=400 Wm−1K−1. At the instant shown, the gas is in thermal equilibrium with the reservoir, the piston is at rest, and the gas occupies volume V0=5.00×10−4 m3V_0 = 5.00× 10^{-4}\ \text{m}^3V0​=5.00×10−4 m3.

Figure dot. Force diagram (piston represented as a dot).

Figure dot

Figure 1. Thermally insulated vertical cylinder with a frictionless piston above a monatomic ideal gas, a copper conduction plate below the gas, and a 300 K water reservoir beneath the plate.

Figure 1
A.

On the dot shown in the force diagram, representing the piston, draw and label the forces that are exerted on the piston. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot.

B.

Derive an expression for the internal energy U0U_0U0​ of the gas in terms of MMM, AAA, V0V_0V0​, PatmP_{\text{atm}}Patm​, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 2. Blank pressure–volume axes for the gas during the interval t₀ ≤ t ≤ t_f.

Figure 2
C.

On Figure 2 provided, sketch the expected relationship between the pressure PPP and volume VVV of the gas for the thermodynamic process that the gas undergoes during the time interval t0≤t≤tft_0 ≤ t ≤ t_ft0​≤t≤tf​. Draw an arrow on your sketch to represent the direction of the thermodynamic process. At time t=t0t=t_0t=t0​, an additional mass m=2.00 kgm = 2.00\ \text{kg}m=2.00 kg is gently placed on the piston. The system is allowed to come to rest at time t=tft=t_ft=tf​. Throughout t0≤t≤tft_0 ≤ t ≤ t_ft0​≤t≤tf​, the copper plate remains in contact with the water reservoir at T0=300 KT_0 = 300\ \text{K}T0​=300 K, and the piston moves slowly enough that the gas remains in thermal equilibrium with the reservoir.

D.

Indicate whether the temperature of the bottom surface of the copper plate (the surface in contact with the gas) is greater than, less than, or equal to T0T_0T0​ during the interval. Check one: During the slow compression in part C, the piston moves downward by Δx=3.00×10−2 m\Delta x = 3.00× 10^{-2}\ \text{m}Δx=3.00×10−2 m in a time interval Δt=40.0 s\Delta t = 40.0\ \text{s}Δt=40.0 s. Assume the gas temperature remains at T0=300 KT_0 = 300\ \text{K}T0​=300 K during this interval. Use g=9.80 m/s2g = 9.80\ \text{m/s}^2g=9.80 m/s2.

Tplate>T0T_{\text{plate}} > T_0Tplate​>T0​
Tplate<T0T_{\text{plate}} < T_0Tplate​<T0​
Tplate=T0T_{\text{plate}} = T_0Tplate​=T0​

Briefly justify your answer by calculating the rate at which energy must be transferred to or from the gas and relating it to conduction through the plate.

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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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