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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 rigid, sealed container of volume V=2.40×10−2 m3V = 2.40\times10^{-2}\ \text{m}^3V=2.40×10−2 m3 holds n=1.00 moln = 1.00\ \text{mol}n=1.00 mol of a monatomic ideal gas. The gas is initially at temperature T0=300 KT_0 = 300\ \text{K}T0​=300 K and pressure P0P_0P0​. A thin rectangular aluminum wall of thickness L=2.0×10−3 mL = 2.0\times10^{-3}\ \text{m}L=2.0×10−3 m and area A=1.5×10−2 m2A = 1.5\times10^{-2}\ \text{m}^2A=1.5×10−2 m2 separates the gas from a large thermal reservoir at constant temperature TR=500 KT_R = 500\ \text{K}TR​=500 K, as shown in Figure 1. The gas and reservoir exchange energy only by thermal conduction through the wall. The aluminum has thermal conductivity k=205 W m−1 K−1k = 205\ \text{W}\,\text{m}^{-1}\,\text{K}^{-1}k=205 Wm−1K−1. Assume the wall has negligible heat capacity, the gas remains uniform in temperature, and the gas remains ideal throughout.

Figure 1. Rigid sealed container of monatomic ideal gas separated from a 500 K thermal reservoir by a thin aluminum wall; heat is conducted from reservoir to gas through the wall.

Figure 1

Figure 2. Molecular-speed distributions at initial state (300 K) and at a later, higher-temperature state; student indicates how the distribution changes.

Figure 2

Figure 3. Direction of the net force on the wall due to gas-molecule collisions at the later time; student indicates direction only.

Figure 3
A.
i.

Complete the following tasks in Figures 2 and 3.

•

In Figure 2, indicate how the distribution of molecular speeds of the gas at a later time T>300 KT > 300\ \text{K}T>300 K compares to the distribution at T0=300 KT_0 = 300\ \text{K}T0​=300 K.

•

In Figure 3, indicate the direction of the net force exerted on the wall by the gas due to molecular collisions at the later time.

ii.

The gas is heated by conduction until it reaches thermal equilibrium with the reservoir at Tf=500 KT_f = 500\ \text{K}Tf​=500 K.

Derive an expression for the final pressure PfP_fPf​ of the gas in terms of nnn, VVV, and TfT_fTf​. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 4. Gas temperature versus time as it warms by conduction toward the 500 K reservoir; t1 marks a specific instant used for the instantaneous conduction rate.

Figure 4
B.

Calculate the magnitude of the instantaneous rate at which energy is transferred by conduction into the gas at time t1t_1t1​ (see Figure 4). At a particular time t1t_1t1​, the gas temperature is T1=350 KT_1 = 350\ \text{K}T1​=350 K. The reservoir remains at TR=500 KT_R = 500\ \text{K}TR​=500 K. Assume heat transfer is only by conduction through the wall and use the conduction model Qt=kA ΔTL\frac{Q}{t} = \frac{kA\,\Delta T}{L}tQ​=LkAΔT​ for the instantaneous rate of energy transfer.

Then calculate the time interval Δt\Delta tΔt required for 1.00×104 J1.00\times10^{4}\ \text{J}1.00×104 J of energy to be transferred into the gas if that rate were constant over the interval.

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Free Response Question Practice

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