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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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FRQ Types & Units

Each FRQ type tests specific skills taught in particular units. Here's why certain units appear for each question type:

This mapping reflects College Board's exam structure - each FRQ type tests specific skills that are taught in particular units.

Practice FRQ 1 of 121/12
1. A rigid, thermally insulating container of volume V=2.50×10−2 m3V = 2.50× 10^{-2}\ \text{m}^3V=2.50×10−2 m3 contains n=1.00 moln = 1.00\ \text{mol}n=1.00 mol of a monatomic ideal gas. Initially the gas is in equilibrium at temperature T1=300 KT_1 = 300\ \text{K}T1​=300 K. The gas is then brought into thermal contact with a large thermal reservoir at temperature TR=450 KT_R = 450\ \text{K}TR​=450 K by placing a flat copper plate of thickness L=2.00×10−3 mL = 2.00× 10^{-3}\ \text{m}L=2.00×10−3 m and area A=1.00×10−2 m2A = 1.00× 10^{-2}\ \text{m}^2A=1.00×10−2 m2 between the reservoir and the gas, as shown in Figure 1. The plate is the only path for energy transfer between the reservoir and the gas. Assume the copper has thermal conductivity k=400 W/(m·K)k = 400\ \text{W/(m·K)}k=400 W/(m·K) and that the temperature at the plate surfaces equals the temperatures of the systems in contact with those surfaces. The gas remains uniform in temperature at all times. The container volume remains constant throughout the process.

Figure 1. Rigid insulating container of monatomic ideal gas connected to a 450 K thermal reservoir only through a copper conduction plate (not to scale).

Black-and-white physics apparatus diagram with clean lines and clear labels, drawn as a left-to-right cross-sectional schematic. Overall layout (left to right): - Left region: a rigid rectangular container holding an ideal gas. - Middle: a flat vertical copper plate forming the ONLY shared boundary between the gas and the reservoir. - Right region: a large thermal reservoir. Rigid container (left side): - Draw a rectangle occupying the left half of the figure. - The left wall, top wall, and bottom wall of this rectangle are drawn thicker than normal lines to emphasize insulation and rigidity. - Place the label "Rigid, thermally insulating container" centered above the container. - Inside the container, write the gas state text as a three-line block centered within the gas region: 1) "Monatomic ideal gas" 2) "n = 1.00 mol" 3) "V = 2.50×10^-2 m^3 (constant)" - Also inside the gas region, near the upper-left interior corner, place the label "T_g". - Near the lower-left interior corner, place the initial temperature label "T1 = 300 K". Copper plate (middle barrier): - At the right boundary of the gas container, draw a narrow vertical rectangle representing the copper plate. This plate spans exactly from the container’s bottom interior edge to the container’s top interior edge, so it completely blocks direct contact between gas and reservoir. - Label the plate "Copper plate" centered on the plate. - Add two dimension callouts: - Thickness: draw a short horizontal double-headed arrow crossing the plate from its left face to its right face, labeled "L = 2.00×10^-3 m". - Area: place the text "A = 1.00×10^-2 m^2" adjacent to the plate (to the right of the plate, vertically centered). - Add the thermal conductivity label "k = 400 W/(m·K)" directly below the area label, still adjacent to the plate. Thermal reservoir (right side): - To the immediate right of the copper plate, draw a large rectangular region occupying the right half of the figure. - Fill this region with a light, uniform stipple or pale shading to distinguish it from the gas container (do not obscure text). - Center the label "Large thermal reservoir" near the top of this region. - Place the temperature label "T_R = 450 K" centered in the reservoir region. Contact surfaces and energy-transfer path emphasis: - Draw the copper plate flush against both the gas and reservoir regions with no gaps. - Add a note beneath the plate, centered under it: "Only path for energy transfer is conduction through the copper plate."

Figure 2. Direction of net energy transfer by conduction at the initial moment of contact (T_R = 450 K, gas initially at T1 = 300 K).

A simplified close-up conduction diagram with three adjacent vertical regions arranged left-to-right. Regions (left to right), each taking roughly one-third of the width: 1) Left region: the gas in the container. - Draw a rectangular box labeled at its top: "Gas (initially)". - Inside this left box, write "T1 = 300 K". 2) Middle region: the copper plate. - Draw a thin vertical rectangle between the two boxes, labeled "Copper plate". - On or just below this plate, include the thickness label "L = 2.00×10^-3 m". 3) Right region: the reservoir. - Draw a rectangular box labeled at its top: "Thermal reservoir". - Inside this right box, write "T_R = 450 K". Energy-transfer arrow: - Draw ONE bold horizontal arrow that starts in the reservoir box (right region), passes through the copper plate region, and ends inside the gas box (left region). - The arrow must point strictly from right to left. - Place the label above the arrow, centered over the copper plate: "Net energy transfer by conduction". No other arrows appear in the figure (no bidirectional arrows).

Figure 3. Comparing average molecular speed at 450 K (reservoir) versus 300 K (container gas) at the initial moment.

Comparison diagram with TWO side-by-side square panels of equal size, separated by a small gap, with clear panel titles. Left panel (container gas at initial temperature): - Title centered above: "Container gas". - Inside the square, place the text "T1 = 300 K" near the top edge inside the panel. - Fill the panel with many small identical dots (molecules), evenly scattered. - Select exactly five dots and draw velocity arrows attached to them. - All five arrows are the SAME length within this panel, and they are SHORT. - The arrows point in random directions (not aligned). - Under the panel, centered, write "Average molecular speed: smaller". Right panel (reservoir gas at higher temperature): - Title centered above: "Reservoir gas". - Inside the square, place the text "T_R = 450 K" near the top edge inside the panel. - Fill the panel with many small identical dots (molecules), matching the dot style and approximate dot count density of the left panel. - Select exactly five dots and draw velocity arrows attached to them. - All five arrows are the SAME length within this panel, and they are LONG. - The LONG arrows are exactly twice the length of the SHORT arrows used in the left panel (so the visual comparison is unambiguous). - The arrows point in random directions (not aligned), similar randomness to the left panel. - Under the panel, centered, write "Average molecular speed: larger". Global annotation: - Centered between the two panels (in the gap), add a vertical text label "Same type of gas" to indicate both represent gas molecules (no different particle types). Do not include any mathematical formulas; only the qualitative speed comparison and the exact temperatures.

Figure 4. Constant-volume heating of the gas from T1 = 300 K to TR = 450 K shown on a P–V diagram (V fixed at 2.50×10^-2 m^3).

A P–V graph with explicit numeric axis ranges and a single constant-volume process line. Axes: - Horizontal axis labeled "V (m^3)". - Vertical axis labeled "P (Pa)". - Both axes have arrowheads at the positive ends. Horizontal axis scale (Volume): - Show numeric ticks labeled: 0, 1.00×10^-2, 2.00×10^-2, 3.00×10^-2, 4.00×10^-2. - The tick labeled "2.50×10^-2" must appear as an additional labeled tick between 2.00×10^-2 and 3.00×10^-2 (this is the process volume). Vertical axis scale (Pressure): - Use the ideal gas law values for the two states and place them exactly at labeled tick marks: - Compute and use P1 = nRT1/V = (1.00)(8.314)(300)/(2.50×10^-2) = 9.98×10^4 Pa (shown as "9.98×10^4"). - Compute and use P2 = nRT_R/V = (1.00)(8.314)(450)/(2.50×10^-2) = 1.50×10^5 Pa (shown as "1.50×10^5"). - Show vertical-axis ticks labeled: 0, 5.00×10^4, 1.00×10^5, 1.50×10^5, 2.00×10^5. Process path: - Draw a single solid vertical line (constant volume) exactly above the x-axis tick labeled "2.50×10^-2". - Place two filled circular points on this vertical line: - State 1: at pressure tick "9.98×10^4". Label next to the point: "1" and also "T1 = 300 K". - State 2: at pressure tick "1.50×10^5". Label next to the point: "2" and also "T_R = 450 K". - Draw a small upward arrow along the vertical process line from state 1 toward state 2 to indicate the direction of the process as time passes. No other curves or lines are present. No grid lines.
A.
i. Complete the following tasks in Figures 2 and 3.
• Indicate the direction of the net energy transfer by conduction through the copper plate at the initial moment the plate is placed between the reservoir and the gas in Figure 2.
• Indicate in Figure 3 whether the average molecular speed of the gas molecules in the reservoir is greater than, less than, or equal to the average molecular speed of the gas molecules in the container at the initial moment.
ii. The gas is allowed to come to equilibrium with the reservoir while the volume remains constant, as shown in Figure 4.
Derive an expression for the change in entropy of the gas, ΔSgas\Delta S_{\text{gas}}ΔSgas​, in terms of nnn, the molar heat capacity at constant volume CVC_VCV​, and the initial and final temperatures T1T_1T1​ and TRT_RTR​. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
B. Indicate whether the gas pressure in the container increases, decreases, or remains the same as time passes immediately after thermal contact is established. Consider the initial moment when the plate is put in place and the gas temperature is still T1=300 KT_1 = 300\ \text{K}T1​=300 K while the reservoir remains at TR=450 KT_R = 450\ \text{K}TR​=450 K. Use R=8.31 J/(mol·K)R = 8.31\ \text{J/(mol·K)}R=8.31 J/(mol·K).
______ Increases
______ Decreases
______ Remains the same
Justify your answer in terms of the atomic motion of the gas and how that motion leads to pressure on the container walls.
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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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