Thermal Energy Transfer and Equilibrium AP Physics 2 FRQ – Exam Style Questions etc.
Thermal Energy Transfer and Equilibrium AP Physics 2 FRQ
Unit 9: Thermodynamics
Weightage : 15–18%
Exam Style Practice Questions,Thermal Energy Transfer and Equilibrium AP Physics 2 FRQ
Question
(12 points, suggested time 25 minutes)
In Experiment 1, shown in Figure 1, a sample of an ideal gas is contained in an insulated, sealed chamber with thin, rigid walls. The chamber contains a heater and sensors that measure the temperature and pressure of the gas. A student is asked to design an experiment to determine the number N of molecules of the gas contained in the chamber.
(a) Describe a procedure for collecting data that would allow the student to determine an experimental value for N. Provide enough detail so that a student could replicate the experiment, including any steps necessary to reduce experimental uncertainty.
(b) i. On the following axes, sketch a curve or line to represent the expected relationship between the pressure P and the volume V of the gas while the heater is on. Draw an arrow on the curve or line to represent the direction of the resulting thermal process.
ii. On the following axes, sketch a curve or line to represent the expected relationship between the internal energy U and the volume V of the gas while the heater is on. Draw an arrow on the curve or line to represent the direction of the resulting thermal process.
iii. Briefly justify why the curve or line drawn in part (b)(ii) has the shape that you sketched.
In Experiment 2, shown in Figure 2, a liquid-filled container that is completely wrapped with a material of uniform thickness 0.01 m is inside the sealed chamber that is filled with an ideal gas. The material has a total area of 0.06\(^{m2}\) in contact with the gas. The heater is turned on. As the temperature \(T_{G}\) of the gas increases, the following data for the temperature \(T_{L}\) of the liquid and the rate \(\frac{Q}{\Delta t}\) of energy transfer are collected.
(c) The student is asked to determine an experimental value of the thermal conductivity k of the material used to wrap the container inside the sealed chamber.
i. Indicate what measured and/or calculated quantities could be graphed to yield a straight line that could be used to calculate an experimental value for the thermal conductivity k of the material. Use the blank columns in the table to list any calculated quantities you graph in addition to the data provided.
Vertical Axis: _______________ Horizontal Axis: _______________
ii. Plot the data points for the quantities indicated in part (c)(i) on the graph provided. Clearly scale and label all axes, including units, as appropriate.
iii. Draw the best-fit line for the data graphed in part (c)(ii).
(d) Using the best-fit line, calculate an experimental value for k.
▶️Answer/Explanation
1(a)Example Response
Measure the length, width, and height of the chamber. Activate the heater. Starting at time t = 0 , use the sensors to record the temperature and pressure of the gas every 10s until t = 60s.
1(b)Example Responses
1(c)(Example Response
1(d)Example Response
slope = \(\frac{\Delta y}{\Delta x}\)
slope = \(\frac{\Delta \left ( \frac{Q}{\Delta T} \right )}{\Delta \left ( \Delta T \right )}\)
slope = \(\frac{\left ( \frac{Q}{\Delta T} \right )_{2} -\left ( \frac{Q}{\Delta T} \right )_{1}}{\Delta T_{2}-\Delta T_{1}}\)
slope = \(\frac{\left ( 80 – 44\ \right )\tfrac{j}{s}}{\left ( 220 – 120 \right )K}\)
slope = \(0.36\frac{j}{s.K}\)
\(\frac{Q}{\Delta T} = \frac{kA\Delta T}{L}\)
\(\frac{Q}{\Delta T} = \left ( \frac{kA}{L} \right )\Delta T\)
\(slope =\frac{kA}{L}\)
\(K =\frac{L}{A}\left (slope \right )\)
\(K =\frac{0.01m}{0.06m^{2}}\left ( 0.36\frac{j}{s.K} \right )\)
\(K =0.06\frac{j}{s.K.m}\)
Question
A student gives the following description of a thermodynamic cycle through which a sample of an ideal monatomic gas is taken.
“Initially, the gas has a volume of \(1\times 10^{-3}m^{3}\) and a pressure of \(1\times 10^{5}\) Pa. The gas is in a closed cylinder that has a movable piston on one end. Call the initial state of the gas state A. Process AB takes the gas at constant pressure from state A to state B, where B has three times the volume of state A. The gas is then compressed isothermally until it is back to its initial volume, reaching state C. Finally, a single process CA returns the gas to its initial state A.”
(a) i. On the axes below, plot states A, B, and C, and sketch a graph of pressure P as a function of volume V for cycle ABCA. Label states A, B, and C, and label the axes with numerical values.
ii. Let the temperature for state A be \(T_{0}\). In terms of \(T_{0}\), determine the temperature for state B.
iii. Compare the temperature at state C to the temperature at state A. Explain how your comparison is consistent with your graph above.
(b) i. Briefly describe an experimental procedure that would take the gas from state C to state A.
ii. Relate the temperature of the gas to the microscopic processes involved in the energy transfer as the gas goes from state C to state A for the procedure you described in part (b)(i).
(c) i. Use the student’s verbal description or your graph in part (a)(i) to calculate a numerical value for the work done on the gas in process AB.
ii. The magnitude of the change in internal energy for process AB is \(\mid \Delta U\mid \) = 300 J. Calculate a numerical value for the energy added to or removed from the gas by heating in process AB.
Answer/Explanation
Ans:
(a) i) 
ii) Using the ideal gas law:
For the correct answer: \(T_{B}=3T_{0}\)
iii) \(T_{C}=3T_{0}\)
(b) i) The volume remains constant and describing a valid way to accomplish this in the procedure. The temperature must decrease and describing a valid way to accomplish this in the procedure. Lock the piston in place and put the cylinder in a cool water bath.
ii) The warmer gas (faster molecules) collide with the cooler surroundings (slower molecules). The net energy flow is from the gas to the surroundings which results in cooler gas (slower molecules).
(c) i) \(W=-P\Delta V=-(1\times 10^{5}Pa)(2\times 10^{-3}m^{3})\)
W = -200 J
ii) \(\Delta U\) = Q + W
300 J = Q – 200 J
Q = 500 J
Question: (12 points-suggested time 25 minutes)
A mole of ideal gas is enclosed in a cylinder with a movable piston having a cross-sectional area of 1 x 10-2 m2. The gas is taken through a thermodynamic process, as shown in the figure.
(A) Calculate the temperature of the gas at state A, and describe the microscopic property of the gas that is related to the temperature.
(B) Calculate the force of the gas on the piston at state A, and explain how the atoms of the gas exert this force on the piston.
(C) Predict qualitatively the change in the internal energy of the gas as it is taken from state B to state C. Justify your prediction.
(D) Is heat transferred to or from the gas as it is taken from state B to state C? Justify your answer.
(E) Discuss any entropy changes in the gas as it is taken from state B to state C. Justify your answer.
(F) Calculate the change in the total kinetic energy of the gas atoms as the gas is taken from state C to state A.
(G) On the axis provided, sketch and label the distribution of the speeds of the atoms in the gas for states A and B. Make sure that the two sketches are proportionally accurate.
Answer/Explanation
Ans:
Note that all the numbers in this problem are rounded to two significant digits because that is the accuracy of the data from the graph.
Part (A)
1 point-For the correct value of temperature with supporting equation and work: PV = nRT, T = 480 K.
1 point-For an explanation that the temperature of the gas is directly related to the average kinetic energy of the gas molecules.
Part (B)
1 point-For the correct force with supporting equation and work: F = PA = 2,000 N.
1 point-For an explanation of the mechanism that produces gas force on the piston.
For example: The gas molecules collide with the piston in a momentum collision that imparts a tiny force on the piston. The sum of all the individual molecular collision forces is the net force on the piston.
Part (C)
1 point-For indicating that the temperature of the gas is decreasing and explaining why this occurs.
For example: Since the PV value of the gas decreases, the temperature of the gas decreases in this process as indicated by the ideal gas law.
1 point-For indicating that the internal energy of the gas will decrease and explaining why this occurs.
For example: ΔU = nRΔT and the temperature is decreasing. Therefore, the internal energy of the gas also must decrease.
Part (D)
1 point-For indicating that the work in this process is positive because the process is moving to the left on the graph and that the thermal energy of the gas is decreasing because the temperature is decreasing.
1 point-For using the first law of thermodynamics to determine that heat is being removed from the gas.
For example: work is positive and the gas internal energy is decreasing. Therefore, using the first law of thermodynamics, ΔU = Q + W, we can see that heat must be leaving the gas during this process.
Part (E)
1 point-For indicating that the entropy of the gas is decreasing because thermal energy is being removed in this process. This reduces the spread of
the speed distribution of the gas, thus reducing disorder.
Part (F)
1 point-For the correct answer with supporting work:
Part (G)
Based on the PV values, the temperature at point A is higher than that at point B. Thus, the peak for A must be at a higher speed than for B.
1 point-For both curves showing a roughly bell shape, and curve A having a higher average speed than curve B.
The area under the graphs must be equal because the number of molecules remains the same. This means the peak for A must be lower than that for B.
1 point-For curve A having a lower maximum than curve B, and both curves having roughly the same area beneath them.