AP Physics 2 FRQ Practice

🧲AP Physics 2

Practice FRQ 1 of 121/12

1. A sealed, rigid cylindrical container holds

n = 0.200\ \text{mol}

of an ideal monatomic gas. Initially the gas is in thermal equilibrium at temperature

T_1 = 300\ \text{K}

and has pressure

P_1 = 1.00× 10^5\ \text{Pa}

. The container is fitted with a frictionless piston that can be clamped so the gas volume is fixed, or unclamped so the piston can move and maintain a constant external pressure of

1.00× 10^5\ \text{Pa}

, as shown in Figure 1. The gas is brought into thermal contact with a large thermal reservoir at temperature

T_2 = 450\ \text{K}

. Assume the piston and cylinder are perfectly insulating except where specified, and the gas remains ideal throughout.

Figure 1. Rigid cylinder with frictionless piston in two operating modes: (a) piston clamped (constant volume) and (b) piston unclamped against a constant external pressure of 1.00×10^5 Pa, with the cylinder wall in thermal contact with a reservoir at 450 K.

Black-and-white physics apparatus diagram arranged as two side-by-side subfigures labeled “(a)” on the left and “(b)” on the right.

Common features in both subfigures (same geometry and relative placement):
- A vertical cylindrical container is drawn as a tall rectangle with slightly rounded top corners, occupying the central region of each subfigure.
- Inside each cylinder, the region below the piston is labeled “ideal gas” (text centered in the gas region).
- A horizontal piston disk seals the top of the gas. The piston is drawn as a thick horizontal bar spanning the full inner width of the cylinder.
- Above the piston, a short vertical piston rod extends upward from the center of the piston.
- The piston is explicitly labeled “frictionless piston” with a leader arrow pointing to the piston disk.
- Near the gas region, include a text label “n = 0.200 mol” placed inside the cylinder wall region but not overlapping the gas label.

Subfigure (a): clamped piston (constant volume)
- A clamp mechanism is drawn attached to the outside of the cylinder near the top: a C-shaped bracket on the right side of the cylinder grips the piston rod, preventing vertical motion.
- A bold text label to the right of the cylinder reads: “piston clamped” on one line and directly below it “V = constant”. A leader arrow from this label points to the clamp.
- No external pressure arrow is shown above the piston in (a), emphasizing that the clamp fixes volume.

Subfigure (b): unclamped piston (constant pressure)
- No clamp is drawn anywhere on the piston rod.
- Above the piston, draw multiple evenly spaced downward-pointing arrows (at least three) indicating external pressure acting on the piston.
- Next to these arrows, place a text label: “external pressure” on one line and directly below it “P = 1.00×10^5 Pa”. The label is placed above and slightly to the right of the piston so it does not overlap the arrows.
- To the right of the cylinder, place a bold text label: “piston unclamped” on one line and directly below it “P = constant”.

Thermal reservoir (shown for both subfigures in a consistent way):
- On the far right side of the overall figure (spanning the height of both subfigures), draw a large vertical rectangle labeled “thermal reservoir”.
- Inside that reservoir rectangle, place the temperature label “T2 = 450 K” centered.
- From the reservoir rectangle to the outer wall of each cylinder, draw a short horizontal contact interface (a thin line touching the cylinder wall) to indicate thermal contact; next to each interface, place the label “thermal contact” with a leader arrow pointing to the cylinder wall at the contact location.

Style constraints:
- Use clear, textbook line art with consistent medium-weight outlines.
- All numeric values must appear exactly as: “n = 0.200 mol”, “P = 1.00×10^5 Pa”, and “T2 = 450 K”.

Figure 2. P–V diagram with initial state 1 shown; student indicates constant-volume heating path to final state 2.

A blank P–V graph template with axes, numerical tick labels, and one marked state point.

Axes and layout:
- Horizontal axis labeled “V (m^3)” centered below the axis.
- Vertical axis labeled “P (Pa)” rotated vertically along the left axis.
- Both axes have arrowheads at their positive ends.
- The origin at the bottom-left corner is labeled “0” on both axes.

Tick marks and numeric scale (must be printed as visible tick labels):
- Volume axis: labeled ticks at 0, 1.0×10^−3, 2.0×10^−3, 3.0×10^−3, 4.0×10^−3, 5.0×10^−3.
- Pressure axis: labeled ticks at 0, 1.0×10^5, 2.0×10^5, 3.0×10^5.
- No gridlines.

Initial state point 1 (exact placement and labeling):
- A solid filled dot labeled “1” is placed at the intersection corresponding to P1 = 1.00×10^5 Pa and V1 = 5.0×10^−3 m^3.
- Next to the dot (not overlapping), print a small two-line label: “T1 = 300 K” on the first line and “P1 = 1.00×10^5 Pa” on the second line.

Student-work region and instruction cue (visible text):
- Near the upper right open region of the plot, include the text: “Draw process to point 2 (V constant)”.
- Do NOT draw the process path or point 2; leave the rest of the graph empty.

Numerical consistency note embedded as a subtle axis note (visible text, small font near bottom):
- Place a small note under the x-axis: “V1 = nRT1/P1 = 5.0×10^−3 m^3”.

Figure 3. P–V diagram with initial state 1 shown; student indicates constant-pressure heating path to final state 2.

i. Complete the following tasks in Figures 2 and 3.

• In Figure 2, the piston is clamped and the gas is heated from

T_1

T_2

at constant volume. Indicate the qualitative path on the

P\text{–}V

diagram and label the final state as point 2.

• In Figure 3, the piston is unclamped and the gas is heated from

T_1

T_2

at constant pressure

P = 1.00× 10^5\ \text{Pa}

. Indicate the qualitative path on the

P\text{–}V

diagram and label the final state as point 2.

ii. For the constant-pressure heating process (piston unclamped), derive an expression for the work done by the gas,

W

, in terms of

n

R

T_1

, and

T_2

. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 4. Conduction through a flat slab separating the gas from a thermal reservoir: slab thickness L, contact area A, hot side at Th (reservoir) and cold side at Tc (gas).

A side-view heat-conduction schematic drawn left-to-right with three main regions: gas, slab, reservoir.

Left region (gas):
- On the left third of the figure, draw a rectangular region labeled “gas”.
- Inside this gas region, place the temperature label “Tc” on one line and directly below it “(gas)” in smaller text.

Middle region (slab):
- Immediately to the right of the gas region, draw a vertical rectangular slab (a tall, thin rectangle) separating gas from reservoir.
- The slab’s left face touches the gas region; the slab’s right face touches the reservoir region with no gap.
- Above the slab, draw a double-headed horizontal arrow spanning exactly from the left face of the slab to the right face of the slab; label this arrow “L” centered above it, indicating slab thickness.
- On the slab’s left face (the face in contact with the gas), draw a short bracket or outline highlighting the contact face; label this face area with “A” using a leader arrow pointing to the face. The label must read exactly “A”.

Right region (thermal reservoir):
- On the right third of the figure, draw a large rectangular region labeled “thermal reservoir”.
- Inside it, place the temperature label “Th” on one line and directly below it “(reservoir)”.
- Also include the explicit numeric reservoir temperature as visible text inside the reservoir region: “Th = 450 K”.

Heat-flow indication:
- Draw a single bold arrow passing horizontally from the reservoir region through the slab toward the gas region (right-to-left arrow direction). Place the label “Q̇” above the arrow.

Styling:
- Clean monochrome line art.
- All labels are clear and non-overlapping: Tc on the gas side, Th and “Th = 450 K” on the reservoir side, L above the slab, A pointing to the slab face in contact with the gas.

B. Indicate whether thermal energy is transferred from the reservoir to the gas, from the gas to the reservoir, or neither. The piston is clamped so the volume remains fixed at its initial value

V_1

. The thermal contact between the gas and the reservoir occurs only through a flat slab (Figure 4) with thermal conductivity

k = 0.80\ \text{W}\,\text{m}^{-1}\,\text{K}^{-1}

, thickness

L = 4.0× 10^{-3}\ \text{m}

, and contact area

A = 2.5× 10^{-2}\ \text{m}^2

. At a particular instant during the heating, the gas temperature is

T_g = 330\ \text{K}

while the reservoir remains at

T_2 = 450\ \text{K}

given_values: ["k = 0.80 W·m^-1·K^-1", "L = 4.0×10^-3 m", "A = 2.5×10^-2 m^2", "T2 = 450 K", "Tg = 330 K"]

______ From the reservoir to the gas
______ From the gas to the reservoir
______ Neither

Justify your answer by calculating the magnitude of the instantaneous rate of energy transfer by conduction through the slab at that instant.

🧲AP Physics 2

Practice FRQ 1 of 121/12

1. A sealed, rigid cylindrical container holds

n = 0.200\ \text{mol}

of an ideal monatomic gas. Initially the gas is in thermal equilibrium at temperature

T_1 = 300\ \text{K}

and has pressure

P_1 = 1.00× 10^5\ \text{Pa}

. The container is fitted with a frictionless piston that can be clamped so the gas volume is fixed, or unclamped so the piston can move and maintain a constant external pressure of

1.00× 10^5\ \text{Pa}

, as shown in Figure 1. The gas is brought into thermal contact with a large thermal reservoir at temperature

T_2 = 450\ \text{K}

. Assume the piston and cylinder are perfectly insulating except where specified, and the gas remains ideal throughout.

Figure 2. P–V diagram with initial state 1 shown; student indicates constant-volume heating path to final state 2.

Figure 3. P–V diagram with initial state 1 shown; student indicates constant-pressure heating path to final state 2.

i. Complete the following tasks in Figures 2 and 3.

• In Figure 2, the piston is clamped and the gas is heated from

T_1

T_2

at constant volume. Indicate the qualitative path on the

P\text{–}V

diagram and label the final state as point 2.

• In Figure 3, the piston is unclamped and the gas is heated from

T_1

T_2

at constant pressure

P = 1.00× 10^5\ \text{Pa}

. Indicate the qualitative path on the

P\text{–}V

diagram and label the final state as point 2.

ii. For the constant-pressure heating process (piston unclamped), derive an expression for the work done by the gas,

W

, in terms of

n

R

T_1

, and

T_2

. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 4. Conduction through a flat slab separating the gas from a thermal reservoir: slab thickness L, contact area A, hot side at Th (reservoir) and cold side at Tc (gas).

B. Indicate whether thermal energy is transferred from the reservoir to the gas, from the gas to the reservoir, or neither. The piston is clamped so the volume remains fixed at its initial value

V_1

. The thermal contact between the gas and the reservoir occurs only through a flat slab (Figure 4) with thermal conductivity

k = 0.80\ \text{W}\,\text{m}^{-1}\,\text{K}^{-1}

, thickness

L = 4.0× 10^{-3}\ \text{m}

, and contact area

A = 2.5× 10^{-2}\ \text{m}^2

. At a particular instant during the heating, the gas temperature is

T_g = 330\ \text{K}

while the reservoir remains at

T_2 = 450\ \text{K}

given_values: ["k = 0.80 W·m^-1·K^-1", "L = 4.0×10^-3 m", "A = 2.5×10^-2 m^2", "T2 = 450 K", "Tg = 330 K"]

______ From the reservoir to the gas
______ From the gas to the reservoir
______ Neither

Justify your answer by calculating the magnitude of the instantaneous rate of energy transfer by conduction through the slab at that instant.

essential ap study content awaits..

Free Response Question Practice

essential ap study content awaits..

Free Response Question Practice