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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 cross-sectional 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. At the instant shown, the gas is in mechanical equilibrium, the piston is at rest, and the gas occupies volume V0=6.00×10−3 m3V_0 = 6.00× 10^{-3}\ \text{m}^3V0​=6.00×10−3 m3. The cylinder walls and piston are good thermal conductors, and the cylinder is surrounded by a large thermal reservoir at constant temperature T0=300 KT_0 = 300\ \text{K}T0​=300 K. The gas may be treated as an ideal gas.

Figure 1. Vertical cylinder of monatomic ideal gas sealed by a frictionless, movable piston in thermal contact with a 300 K reservoir; initial equilibrium state labeled with M, A, P_atm, and V0.

Figure 1

Figure dot. Force diagram. Dot represents the piston; students draw all forces on the piston.

Figure dot
A.

On the Figure dot shown, 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 when it has volume V0V_0V0​, 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 sketching the process from t0 to tf.

Figure 2
C.

On the axes provided in Figure 2, 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 top of the piston. The piston moves downward slowly and comes to rest at time t=tft=t_ft=tf​ while the gas remains in thermal equilibrium with the reservoir at temperature T0T_0T0​ throughout the process.

D.

Indicate whether TnewT_{\text{new}}Tnew​ is greater than, less than, or equal to T0T_0T0​. After the mass mmm is in place and the piston is at rest, the reservoir is replaced by a different large reservoir at constant temperature TnewT_{\text{new}}Tnew​. The gas is allowed to come to thermal equilibrium with the new reservoir while the mass mmm remains on the piston. When equilibrium is reached, the gas volume is measured to be V0V_0V0​.

given_values: ["M=4.00 kgM=4.00\ \text{kg}M=4.00 kg", "m=2.00 kgm=2.00\ \text{kg}m=2.00 kg", "A=2.50×10−3 m2A=2.50× 10^{-3}\ \text{m}^2A=2.50×10−3 m2", "Patm=1.01×105 PaP_{\text{atm}}=1.01× 10^5\ \text{Pa}Patm​=1.01×105 Pa", "V0=6.00×10−3 m3V_0=6.00× 10^{-3}\ \text{m}^3V0​=6.00×10−3 m3", "T0=300 KT_0=300\ \text{K}T0​=300 K"]

Tnew>T0T_{\text{new}} > T_0Tnew​>T0​
Tnew<T0T_{\text{new}} < T_0Tnew​<T0​
Tnew=T0T_{\text{new}} = T_0Tnew​=T0​

Briefly justify your answer by referencing at least one feature of your answers to parts A, B, or C and describing the atomic motion associated with the temperature change.

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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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