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AP Physics 2 Representations FRQ Practice

57 Translation Between Representations questions written in the AP format. Pick one, read the full question, and write your response. Fiveable scores each Representations FRQ response part by part on the AP rubric.

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Your first scored response is included. A plan unlocks unlimited scoring.

New to the Representations FRQ? Read the exam guide

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400 K gas reservoir linked to a weighted piston by a metal rod

Unit 9: Thermodynamics

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A sample of monatomic ideal gas is sealed in a vertical cylinder by a movable piston of mass M=4.0 kgM=4.0\ \text{kg} and cross-sectional area A=2.0×10−3 m2A=2.0× 10^{-3}\ \text{m}^2. 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}. The cylinder is connected at its base to a large thermal reservoir at temperature Th=400 KT_h=400\ \text{K} by a solid metal rod of length L=0.50 mL=0.50\ \text{m}, cross-sectional area Ar=1.0×10−4 m2A_r=1.0× 10^{-4}\ \text{m}^2, and thermal conductivity k=200 W/(m⋅K)k=200\ \text{W/(m}\cdot\text{K)}. Initially, the gas is in thermal equilibrium with the reservoir, the piston is at rest, and the gas occupies volume V0=1.6×10−3 m3V_0=1.6× 10^{-3}\ \text{m}^3, as shown in Figure 1.

Figure 1. Gas in a vertical cylinder with a movable piston and a conducting rod connected to a hot thermal reservoir (initial state).

Figure 1

Figure dot. Force diagram (piston).

Figure dot
A.

On the dot shown in Figure dot, 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_0 of the gas in its initial state in terms of MM, AA, V0V_0, PatmP_{\text{atm}}, and physical constants, as appropriate. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 2. P–V axes for the thermodynamic process from t0 to tf.

Figure 2
C.

On the axes provided in Figure 2, sketch the expected relationship between the pressure PP and volume VV of the gas for the thermodynamic process that the gas undergoes during the time interval t0≤t≤tft_0≤ t≤ t_f. Draw an arrow on your sketch to represent the direction of the thermodynamic process. At time t=t0t=t_0, an additional mass m=2.0 kgm=2.0\ \text{kg} is gently placed on top of the piston. The system is allowed to come to rest and reach thermal equilibrium with the reservoir at temperature ThT_h at time t=tft=t_f.

D.

Indicate whether the total entropy change of the gas, ΔSgas\Delta S_{\text{gas}}, during t0≤t≤tft_0≤ t≤ t_f is greater than, less than, or equal to zero. During the interval t0≤t≤tft_0≤ t≤ t_f, the gas is maintained at the constant temperature Th=400 KT_h=400\ \text{K}. The initial volume is V0=1.6×10−3 m3V_0=1.6× 10^{-3}\ \text{m}^3. The piston area is A=2.0×10−3 m2A=2.0× 10^{-3}\ \text{m}^2. The masses are M=4.0 kgM=4.0\ \text{kg} and m=2.0 kgm=2.0\ \text{kg}. The atmospheric pressure is Patm=1.01×105 PaP_{\text{atm}}=1.01× 10^{5}\ \text{Pa}. Use g=9.8 m/s2g=9.8\ \text{m/s}^2.

given_values: ["Th=400 KT_h=400\ \text{K}", "V0=1.6×10−3 m3V_0=1.6× 10^{-3}\ \text{m}^3", "A=2.0×10−3 m2A=2.0× 10^{-3}\ \text{m}^2", "M=4.0 kgM=4.0\ \text{kg}", "m=2.0 kgm=2.0\ \text{kg}", "Patm=1.01×105 PaP_{\text{atm}}=1.01× 10^{5}\ \text{Pa}", "g=9.8 m/s2g=9.8\ \text{m/s}^2"]

ΔSgas>0\Delta S_{\text{gas}}>0
ΔSgas<0\Delta S_{\text{gas}}<0
ΔSgas=0\Delta S_{\text{gas}}=0

Briefly justify your answer by referencing at least one feature of your answers to parts A, B, or C, and by using an appropriate thermodynamic relationship.

What the Representations FRQ asks

The Translation Between Representations (TBR) question is FRQ 2 on the AP Physics 2 exam. You describe one scenario with a diagram, a derivation, and a graph, then reach a final result, usually one you indicate and justify.

25–30 min
suggested on the exam
12 points
across parts A to D
95 min
for all four FRQs
read the exam guide

  1. Part A: Representation

    A diagram or other representation of the scenario

    3 pts

  2. Part B: Derivation

    An expression derived from a fundamental principle

    4 pts

  3. Part C: Graph

    Sketch how one quantity changes with another

    3 pts

  4. Part D: Result

    A final result, usually one you indicate and justify

    2 pts

Representations FRQ skill sheet

Every rubric point on one page: what earns it, what to do and what to avoid. Tap the sheet to see it full size.

How to Write the AP Physics 2 Representations FRQ

How Representations FRQ practice works

Each question follows the exam’s format, from the full prompt to a score on every part.

  1. Read the full question

    The scenario, its figures, and all four parts, A through D, laid out the way the exam shows them.

  2. Write on a 27-minute timer

    Inside the 25 to 30 minutes the exam suggests for this question. Pause it or turn it off, and your response saves as you go.

  3. Submit for a score out of 12

    Your response is scored against the scoring guidelines written for that question. Your first score is included.

Feedback on every part

A summary at the top tells you what to work on next. Below it, each part shows whether you earned the point and what the scoring guidelines were looking for.

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Detailed Feedback

Part A: 0/1 point

Did not earn the point. You did not provide a drawing on the energy-level diagram. To earn this point, you needed to draw an arrow starting at the n = 4 energy level.

Part B: 1/1 point

Earned the point. You correctly began your derivation by stating the fundamental equations for photon energy (E = hc/λ) and the energy levels of hydrogen.

Part B: 1/1 point

Earned the point. You correctly wrote the expression for the energy difference between the two hydrogen levels in terms of ni and nf.

Detailed feedback on a practice Representations FRQ

Questions about the Representations FRQ

How many responses can I get scored?

You can read every question without a plan. Your first scored response is included. A plan unlocks unlimited scoring.

How do I draw the diagrams and graphs?

Open the drawing tool in the editor and draw them there. You can also switch to handwrite and add a photo of your page.

How is the TBR different from the Mathematical Routines question?

Both include a derivation. The TBR also asks for a diagram and a graph, and ends with a result you justify. It’s worth 12 points instead of 10.

How do I type equations and symbols?

Use the subscript, superscript, and special-character buttons in the editor toolbar. Or write your derivation on paper, switch to handwrite, and add a photo.

Are these real College Board questions?

No. We wrote them in the AP format, with the same four parts, and wrote scoring guidelines for each one.

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AP Physics 2 FRQs

Every FRQ type for AP Physics 2, with practice for each.

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AP Physics 2 study guides

Unit-by-unit review for the whole course.

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