AP Physics 2: Algebra-Based Unit 1: Thermodynamics Practice Exam

Assessment for Unit 1: Thermodynamics

Estimated Time: 73 minutes

Exam Details

Questions: 73 total (73 multiple choice)
Time: 73 minutes (recommended)
Topics Covered: Unit 1: Thermodynamics
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (73 Questions)

Select the one best answer for each question.

1. [Skill: 7.A | Topic: 1.1] A rigid, sealed container is filled with an ideal gas. A heater is used to increase the temperature of the gas. Which of the following statements best describes the microscopic cause for the observed increase in the gas pressure?

(A)The gas atoms expand in size, causing them to occupy more volume and strike the walls more frequently.(B)The average kinetic energy of the atoms increases, resulting in more frequent and more forceful collisions with the container walls.(C)The intermolecular attractive forces between the atoms increase, pulling them toward the walls with greater acceleration.(D)The number of atoms in the container increases as the temperature rises, leading to a higher density and more collisions.

2. [Skill: 1.4 | Topic: 1.1] A gas is contained in a cylinder with a movable piston. An experimenter slowly pushes the piston down, decreasing the volume of the gas while keeping the temperature constant. Which of the following best explains why the pressure exerted by the gas increases? [Image Cue]: Diagram of a cylinder with a piston. Arrows show the piston moving downward. Inside the cylinder, small dots represent gas particles with velocity vectors of constant length.

(A)The atoms move faster because the piston does work on them, increasing the force of each collision.(B)The atoms collide with the walls more frequently because they have less distance to travel between the container walls.(C)The surface area of the container increases, which decreases the pressure for a constant force.(D)The density of the gas decreases, allowing atoms to move more freely and strike the piston with greater momentum.

3. [Skill: 1.1 | Topic: 1.2] A sample of an ideal gas is contained in a cylinder with a movable piston. Which of the following best describes the microscopic assumptions of the ideal gas model for this sample?

(A)The atoms of the gas exert attractive forces on each other at all times, causing the pressure to be lower than in a real gas.(B)The volume of the individual gas atoms is considered negligible compared to the total volume of the cylinder.(C)Collisions between gas atoms and the walls of the cylinder are inelastic, resulting in a loss of kinetic energy over time.(D)The atoms move in predictable, non-random paths determined by the initial temperature of the gas.

4. [Skill: 5.1 | Topic: 1.2] A student performs an experiment to investigate the relationship between the pressure and temperature of a fixed volume of gas. The student plots the pressure $P$ as a function of temperature $T$ in degrees Celsius ($^\circ C$), as shown in the description of the graph below. How can the value of absolute zero be determined from this graph? [Image Cue]: Line graph, Pressure vs. Temperature, y-axis is Pressure $P$ (Pa), x-axis is Temperature $T$ ($^\circ C$). The data points form a straight line with a positive slope and a positive y-intercept.

(A)Absolute zero is the value of the y-intercept where the temperature is $0^\circ C$.(B)Absolute zero is found by calculating the slope of the line, which represents the gas constant $R$.(C)Absolute zero is the x-intercept found by extrapolating the linear graph to the point where $P = 0$.(D)Absolute zero is the temperature at which the pressure of the gas reaches $1.01 \times 10^5 \text{ Pa}$.

5. [Skill: 2.2 | Topic: 1.2] A sample of an ideal gas is initially in a state with pressure $P_0$, volume $V_0$, and absolute temperature $T_0$. The gas is heated at a constant pressure until its absolute temperature is $2T_0$. The gas is then compressed at a constant temperature until its pressure is $2P_0$. What is the final volume of the gas in terms of $V_0$?

(A)$V_0/2$(B)$V_0$(C)$2V_0$(D)$4V_0$

6. [Skill: 1.A | Topic: 1.3] A block of aluminum at a temperature of $450\text{ K}$ is placed in direct physical contact with an identical block of aluminum at a temperature of $310\text{ K}$. The two-block system is enclosed in an ideal insulating container. Which of the following statements correctly describes the initial transfer of energy between the blocks?

(A)Energy is transferred from the $450\text{ K}$ block to the $310\text{ K}$ block primarily through the process of convection.(B)Energy is transferred from the $450\text{ K}$ block to the $310\text{ K}$ block primarily through the process of conduction.(C)Energy is transferred from the $310\text{ K}$ block to the $450\text{ K}$ block because the lower-temperature block has a greater capacity to absorb energy.(D)There is no initial net transfer of energy because the blocks are made of the same material.

7. [Skill: 5.A | Topic: 1.3] An experimenter monitors the temperature of two substances, $S_1$ and $S_2$, placed in thermal contact within a calorimeter. The data collected is shown in the table below: | Time ($s$) | Temperature of $S_1$ ($^{\circ}\text{C}$) | Temperature of $S_2$ ($^{\circ}\text{C}$) | | :--- | :--- | :--- | | 0 | 85 | 15 | | 100 | 60 | 30 | | 200 | 45 | 40 | | 300 | 42 | 42 | | 400 | 42 | 42 | Which of the following best explains the state of the system at $t = 350\text{ s}$?

(A)The system has reached thermal equilibrium because the net energy transfer between $S_1$ and $S_2$ is zero.(B)The system has reached thermal equilibrium because all molecular motion within the substances has ceased.(C)Thermal energy transfer is still occurring spontaneously from $S_1$ to $S_2$ because $S_1$ was initially hotter.(D)The system is no longer in thermal contact, preventing further energy exchange.

8. [Skill: 1.B | Topic: 1.3] A hot metal sphere is suspended by a thin silk thread inside a glass bulb from which all air has been evacuated (a vacuum). A student observes that the temperature of the glass bulb's outer surface begins to rise. Which of the following statements best justifies this observation?

(A)Energy is transferred from the sphere to the glass via conduction through the silk thread only.(B)Energy is transferred from the sphere to the glass via convection currents of the remaining trace gases.(C)Energy is transferred from the sphere to the glass via radiation, which does not require a medium.(D)Energy cannot be transferred to the glass because thermal contact requires a solid or liquid bridge.

9. [Skill: 2.2 | Topic: 1.4] A sample of $2.0\text{ mol}$ of an ideal monatomic gas is confined to a rigid container. The initial internal energy of the gas is $U_{initial}$. If the absolute temperature of the gas is increased from $300\text{ K}$ to $900\text{ K}$, what is the final internal energy $U_{final}$ of the gas in terms of $U_{initial}$?

(A)$U_{final} = \frac{1}{3}U_{initial}$(B)$U_{final} = \sqrt{3}U_{initial}$(C)$U_{final} = 3U_{initial}$(D)$U_{final} = 9U_{initial}$

10. [Skill: 5.1 | Topic: 1.4] An ideal gas is taken from state $1$ to state $2$ along an isobaric path as shown in the $PV$ diagram. Which of the following correctly identifies the sign of the work $W$ done ON the gas and the sign of the change in internal energy $\Delta U$ for this process? [Image Cue]: PV diagram showing a horizontal line extending from $(V_0, P_0)$ at state 1 to $(3V_0, P_0)$ at state 2. The horizontal axis is Volume $V$ and the vertical axis is Pressure $P$.

(A)$W$ is positive; $\Delta U$ is positive(B)$W$ is positive; $\Delta U$ is negative(C)$W$ is negative; $\Delta U$ is positive(D)$W$ is negative; $\Delta U$ is negative

11. [Skill: 6.4 | Topic: 1.4] A cylinder with a frictionless, movable piston contains a sample of ideal gas. The cylinder is wrapped in a thick layer of insulating material. A piston is rapidly pushed inward, compressing the gas. Which of the following best explains the change in the internal energy of the gas?

(A)The internal energy increases because the work done on the gas is positive and the heat transfer is zero.(B)The internal energy decreases because the gas does work on the surroundings during compression.(C)The internal energy remains constant because the insulation prevents heat from entering or leaving the system.(D)The internal energy remains constant because the work done on the gas is exactly balanced by the heat leaving the system.

Refer to the figure below.

12. [Skill: 5.1 | Topic: 1.5] Two samples of different liquid substances, Sample X and Sample Y, both have a mass of 0.5 kg and are initially at 20°C. Both samples are heated by identical electric immersion heaters that transfer energy to the liquids at a constant rate. The graph below shows the temperature of each sample as a function of time. [Image Cue]: Line graph, Temperature vs. Time, Y-axis labeled 'Temperature (Celsius)', X-axis labeled 'Time (seconds)'. Two lines originate at (0, 20). Line X has a steeper positive slope than Line Y. Based on the data, which of the following correctly compares the specific heat capacities $c_X$ and $c_Y$ of the two substances?

(A)$c_X > c_Y$ because Sample X reaches a higher temperature in the same amount of time.(B)$c_X < c_Y$ because Sample X requires less energy to achieve the same temperature change as Sample Y.(C)$c_X = c_Y$ because both samples were heated by identical heaters for the same duration.(D)$c_X < c_Y$ because the rate of energy transfer is inversely proportional to the final temperature reached.

13. [Skill: 2.2 | Topic: 1.5] A cylindrical metal rod of length $L$ and cross-sectional area $A$ connects two thermal reservoirs at temperatures $T_H$ and $T_C$, where $T_H > T_C$. The rate of steady-state heat conduction through this rod is $H$. If the rod is replaced by a second rod made of the same material but with length $2L$ and radius $2r$ (where $A = \pi r^2$), what is the new rate of heat conduction $H'$ in terms of $H$?

(A)$H' = H/2$(B)$H' = H$(C)$H' = 2H$(D)$H' = 4H$

14. [Skill: 6.2 | Topic: 1.5] A student places one end of a copper rod and one end of a wooden rod of identical dimensions into a container of boiling water. After one minute, the end of the copper rod not in the water feels significantly hotter than the corresponding end of the wooden rod. Which of the following best explains this difference in terms of the microscopic properties of the materials?

(A)Copper atoms have a lower mass than the molecules in wood, allowing them to vibrate at higher frequencies.(B)The specific heat of copper is much higher than that of wood, allowing it to move energy more quickly.(C)Copper possesses a high concentration of free electrons that can move through the metal lattice and transfer kinetic energy via collisions.(D)The wooden rod acts as a blackbody radiator, emitting the energy away from the rod faster than the copper rod can conduct it.

15. [Skill: 1.4 | Topic: 1.1] A sample of an ideal gas is confined within a rigid container of fixed volume. The absolute temperature of the gas is increased from $T$ to $2T$. Which of the following best describes the microscopic cause for the change in the pressure exerted by the gas on the container walls?

(A)The average kinetic energy of the gas atoms doubles, which increases both the average impulse delivered per collision and the frequency of collisions with the walls.(B)The root-mean-square speed of the gas atoms doubles, which results in the atoms hitting the walls with twice the momentum.(C)The atoms of the gas expand in size due to the increased temperature, which increases the total surface area of the atoms striking the walls.(D)The atoms move in more direct, linear paths toward the walls rather than chaotic motion, increasing the perpendicular component of the force $F_{\perp}$.

16. [Skill: 6.4 | Topic: 1.6] A hot metal bolt is dropped into a beaker of room-temperature water that is kept inside a perfectly thermally insulated container. The bolt and the water are allowed to reach thermal equilibrium. Which of the following correctly describes the change in entropy of the bolt-water system and the change in the amount of energy available to do work as a result of this process?

(A)The entropy of the system increases, and the energy available to do work decreases.(B)The entropy of the system increases, and the energy available to do work increases.(C)The entropy of the system remains constant because the container is insulated, and the energy available to do work remains constant.(D)The entropy of the system decreases because the bolt cools down, and the energy available to do work decreases.

17. [Skill: 6.4 | Topic: 1.6] A solid metal cube at temperature $T_1$ is placed in thermal contact with an identical metal cube at temperature $T_2$, where $T_1 > T_2$. The two-cube system is contained within a perfectly thermally insulated container. Which of the following best describes the change in entropy for the cubes and the total system from the moment of contact until the cubes reach a final equilibrium temperature $T_f$?

(A)The entropy of the cube at $T_1$ decreases, the entropy of the cube at $T_2$ increases, and the total entropy of the system increases.(B)The entropy of the cube at $T_1$ decreases, the entropy of the cube at $T_2$ increases, and the total entropy of the system remains constant because the system is isolated.(C)The entropy of the cube at $T_1$ increases, the entropy of the cube at $T_2$ decreases, and the total entropy of the system remains constant.(D)The entropy of both cubes increases because the thermal energy is now dispersed across a larger combined volume, leading to a total increase in system entropy.

18. [Skill: 1.4 | Topic: 1.6] A small block of hot metal at an initial temperature $T_H$ is placed inside a thermally insulated container filled with a larger mass of cool water at an initial temperature $T_C$. The system, consisting of the metal block and the water, is allowed to reach thermal equilibrium at a final temperature $T_F$. Which of the following correctly describes the change in entropy for the metal block and the total change in entropy for the system (block + water) during this process?

(A)The entropy of the metal block decreases, and the total entropy of the system increases.(B)The entropy of the metal block increases, and the total entropy of the system increases.(C)The entropy of the metal block decreases, and the total entropy of the system remains constant.(D)The entropy of the metal block remains constant, and the total entropy of the system increases.

19. [Skill: 6.4 | Topic: 1.6] A block of hot copper at temperature $T_H$ is placed into a thermally insulated container filled with an equal mass of water at a lower temperature $T_C$. The copper and water are allowed to reach thermal equilibrium at a final temperature $T_F$. Which of the following correctly describes the change in entropy for the copper block and the total change in entropy for the entire copper-water system?

(A)The entropy of the copper block decreases, and the total entropy of the system increases.(B)The entropy of the copper block increases, and the total entropy of the system increases.(C)The entropy of the copper block decreases, and the total entropy of the system remains constant.(D)The entropy of the copper block increases, and the total entropy of the system remains constant.

20. [Skill: 1.4 | Topic: 1.6] A metal block at temperature $T_H$ is placed inside a thermally insulated container filled with water at a lower temperature $T_C$. The block and water are allowed to reach thermal equilibrium. Which of the following correctly describes the changes in entropy for the block, the water, and the combined block-water system? (A) The entropy of the block decreases, the entropy of the water increases, and the total entropy of the system increases. (B) The entropy of the block increases, the entropy of the water decreases, and the total entropy of the system remains constant. (C) The entropy of the block decreases, the entropy of the water increases, and the total entropy of the system remains constant. (D) The entropy of the block increases, the entropy of the water decreases, and the total entropy of the system increases.

(A)The entropy of the block decreases, the entropy of the water increases, and the total entropy of the system increases.(B)The entropy of the block increases, the entropy of the water decreases, and the total entropy of the system remains constant.(C)The entropy of the block decreases, the entropy of the water increases, and the total entropy of the system remains constant.(D)The entropy of the block increases, the entropy of the water decreases, and the total entropy of the system increases.

21. [Skill: 6.4 | Topic: 1.6] A small, hot metal cube of mass $m$ and initial temperature $T_H$ is placed into a large, thermally insulated container filled with a cold liquid of mass $M$ at temperature $T_C$ (where $T_C < T_H$). The container is then sealed, forming an isolated system. After a long period of time, the cube and the liquid reach thermal equilibrium at a final temperature $T_E$. Which of the following correctly describes the changes in entropy for the cube and the total isolated system during this process?

(A)The entropy of the cube decreases, and the total entropy of the system increases.(B)The entropy of the cube increases, and the total entropy of the system remains constant.(C)The entropy of the cube decreases, and the total entropy of the system remains constant.(D)The entropy of the cube increases, and the total entropy of the system increases.

22. [Skill: 7.2 | Topic: 1.6] A hot metal block at temperature $T_H$ is placed in thermal contact with a cold metal block at temperature $T_L$ inside a well-insulated container. The blocks are allowed to reach thermal equilibrium. Which of the following correctly describes the change in entropy for the hot block and the total system consisting of both blocks? (A) The entropy of the hot block decreases, and the total entropy of the system increases. (B) The entropy of the hot block increases, and the total entropy of the system increases. (C) The entropy of the hot block decreases, and the total entropy of the system remains constant. (D) The entropy of the hot block increases, and the total entropy of the system remains constant.

(A)The entropy of the hot block decreases, and the total entropy of the system increases.(B)The entropy of the hot block increases, and the total entropy of the system increases.(C)The entropy of the hot block decreases, and the total entropy of the system remains constant.(D)The entropy of the hot block increases, and the total entropy of the system remains constant.

23. [Skill: 7.A | Topic: 1.6] An insulated container holds two compartments separated by a removable partition. Side $X$ contains an ideal gas at temperature $T_H$, and Side $Y$ contains the same species of ideal gas at a lower temperature $T_L$. The partition is removed, and the gases are allowed to reach thermal equilibrium. Which of the following best describes the change in entropy and the availability of energy to do work for this isolated system? (A) The total entropy increases because energy has dispersed more widely, and the amount of energy available to do work decreases. (B) The total entropy increases because the volume for each gas has increased, and the amount of energy available to do work increases. (C) The total entropy remains constant because the container is perfectly insulated, and the amount of energy available to do work remains constant. (D) The total entropy remains constant because the total internal energy of the isolated system is conserved, and the amount of energy available to do work decreases.

(A)The total entropy increases because energy has dispersed more widely, and the amount of energy available to do work decreases.(B)The total entropy increases because the volume for each gas has increased, and the amount of energy available to do work increases.(C)The total entropy remains constant because the container is perfectly insulated, and the amount of energy available to do work remains constant.(D)The total entropy remains constant because the total internal energy of the isolated system is conserved, and the amount of energy available to do work decreases.

24. [Skill: 6.4 | Topic: 1.6] A hot metal block at temperature $T_H$ is placed in thermal contact with a cold metal block at temperature $T_C$. The two blocks are contained within a perfectly thermally insulated box. After a long period of time, the blocks reach thermal equilibrium at a final temperature $T_F$. Which of the following correctly describes the changes in entropy for the individual blocks and the two-block system during this process?

(A)The entropy of the hot block decreases, the entropy of the cold block increases, and the total entropy of the two-block system increases.(B)The entropy of the hot block decreases, the entropy of the cold block increases, and the total entropy of the two-block system remains constant.(C)The entropy of both blocks increases, resulting in an increase in the total entropy of the two-block system.(D)The entropy of the hot block increases, the entropy of the cold block decreases, and the total entropy of the two-block system remains constant.

25. [Skill: 6.4 | Topic: 1.6] A student performs an experiment where a block of aluminum at a temperature of $400\text{ K}$ is placed in direct contact with an identical block of aluminum at $300\text{ K}$. The two blocks are contained within a perfectly insulated box. The blocks are allowed to reach thermal equilibrium. Which of the following claims correctly describes the change in entropy for the blocks and the system? (A) The entropy of the $400\text{ K}$ block increases because energy is transferred to the $300\text{ K}$ block, causing the particles in the system to move more randomly. (B) The entropy of the $300\text{ K}$ block decreases because the energy it receives becomes more concentrated as the temperature of the block rises. (C) The total entropy of the two-block system remains constant because the box is perfectly insulated, preventing energy from being transferred to the environment. (D) The total entropy of the two-block system increases because the transfer of energy from a high-temperature object to a low-temperature object results in a wider dispersal of energy.

(A)The entropy of the $400\text{ K}$ block increases because energy is transferred to the $300\text{ K}$ block, causing the particles in the system to move more randomly.(B)The entropy of the $300\text{ K}$ block decreases because the energy it receives becomes more concentrated as the temperature of the block rises.(C)The total entropy of the two-block system remains constant because the box is perfectly insulated, preventing energy from being transferred to the environment.(D)The total entropy of the two-block system increases because the transfer of energy from a high-temperature object to a low-temperature object results in a wider dispersal of energy.

26. A sample of an ideal gas is held in a rigid container of fixed volume. If the absolute temperature of the gas is increased by a factor of 4, which of the following correctly describes the resulting changes in the root-mean-square speed ($v_{rms}$) of the gas particles and the pressure ($P$) exerted on the container walls?

(A)The $v_{rms}$ doubles, and the pressure $P$ quadruples.(B)The $v_{rms}$ quadruples, and the pressure $P$ quadruples.(C)The $v_{rms}$ doubles, and the pressure $P$ doubles.(D)The $v_{rms}$ quadruples, and the pressure $P$ doubles.

27. Container A contains Helium gas (molar mass $\approx 4$ g/mol) and Container B contains Oxygen gas (molar mass $\approx 32$ g/mol). Both containers are maintained at the same equilibrium temperature $T$. Which of the following statements accurately compares the microscopic properties of the two gases?

(A)The Helium atoms have a higher average kinetic energy than the Oxygen molecules.(B)The Oxygen molecules have a higher average kinetic energy than the Helium atoms.(C)The root-mean-square speed of the Helium atoms is $\sqrt{8}$ times the root-mean-square speed of the Oxygen molecules.(D)The root-mean-square speed of the Helium atoms is 8 times the root-mean-square speed of the Oxygen molecules.

28. [Image Cue]: A diagram shows a piston-cylinder assembly containing gas particles. Arrows indicate the particles moving and colliding with the piston surface. In the second frame, the piston has moved downward, reducing the volume while the temperature is kept constant. A gas is compressed isothermally (at constant temperature) by a piston. As the volume decreases, the pressure of the gas increases. Which of the following best explains this increase in pressure from a microscopic perspective?

(A)The average force exerted by an individual particle during a single collision increases because the particles are moving faster.(B)The number of particle collisions per unit area of the container wall per unit time increases.(C)The particles lose less energy during collisions with the walls because the walls are closer together.(D)The perpendicular component of the velocity of the atoms increases as the volume of the container is reduced.

29. [Skill: 1.1 | Topic: 1.2] Which of the following statements correctly identifies a fundamental assumption of the classical ideal gas model regarding the microscopic behavior and properties of the gas particles?

(A)The particles exert significant long-range attractive forces on one another between collisions.(B)The total volume occupied by the individual gas particles is negligible compared to the total volume of the container.(C)Collisions between gas particles are inelastic, resulting in a net loss of kinetic energy over time.(D)The particles move in predictable, non-random paths determined by the initial conditions of the system.

30. [Skill: 5.1 | Topic: 1.2] A sample of $n$ moles of an ideal gas is confined in a rigid container of fixed volume $V$. A student measures the pressure $P$ of the gas as the absolute temperature $T$ (in Kelvins) is varied. Which of the following graphs best represents the relationship between $P$ and $T$ for this process?

(A)A horizontal line with a non-zero $P$-intercept.(B)A linear graph with a positive slope that passes through the origin $(0,0)$.(C)A linear graph with a negative slope and a positive $P$-intercept.(D)A hyperbola where $P$ is inversely proportional to $T$.

31. [Skill: 2.2 | Topic: 1.2] A student performs an experiment where the pressure $P$ of a fixed amount of gas in a constant-volume container is measured at various temperatures $T$ in degrees Celsius ($^{\circ}C$). The student plots the data and finds a linear relationship. By extrapolating the line to the point where the pressure $P$ is zero, which of the following can the student determine?

(A)The boiling point of the gas at standard atmospheric pressure.(B)The value of the universal gas constant $R$ in units of $J/(mol \cdot K)$.(C)The numerical value of absolute zero on the Celsius scale.(D)The mass of a single atom of the gas.

32. [Skill: 6.B | Topic: 1.3] Block X at a temperature of $80^\circ C$ and Block Y at a temperature of $20^\circ C$ are placed in thermal contact inside an ideal, perfectly insulated container. Which of the following statements correctly describes the behavior of the system as it approaches a stable state?

(A)Energy is transferred from Block X to Block Y because Block X has a higher temperature, and transfer continues until Block Y reaches $80^\circ C$.(B)Energy is transferred from Block X to Block Y until both blocks reach the same intermediate temperature and the net energy transfer is zero.(C)Energy is transferred from Block Y to Block X because Block Y has a lower internal energy, increasing the total energy of the system.(D)No energy is transferred between the blocks because they are made of different materials with different specific heat capacities.

33. [Skill: 1.C | Topic: 1.3] A student suspends a hot copper sphere using a thin, insulating silk thread inside a transparent glass container from which all air has been evacuated (a vacuum). The student observes that the temperature of the sphere decreases over time. Which mechanism of thermal energy transfer is primarily responsible for this observation?

(A)Conduction through the remaining air molecules in the container.(B)Convection currents established by the density differences of the copper atoms.(C)Radiation emitted by the sphere in the form of electromagnetic waves.(D)Conduction through the silk thread, which acts as a perfect thermal conductor.

34. [Skill: 1.A | Topic: 1.3] [Image Cue]: Line graph, Temperature vs. Time. Object A starts at $T = 90^\circ C$ and curves downward. Object B starts at $T = 10^\circ C$ and curves upward. The two lines meet and become a single horizontal line at $T = 40^\circ C$ at time $t = t_{eq}$. Two objects, A and B, are placed in thermal contact at time $t = 0$. The graph above shows their temperatures as a function of time. Which of the following is a correct interpretation of the state of the system for $t > t_{eq}$?

(A)The objects have reached thermal equilibrium, and the microscopic energy exchange between them has stopped entirely.(B)The objects have reached thermal equilibrium, meaning the rate of energy transfer from A to B equals the rate of energy transfer from B to A.(C)Object A has a higher specific heat than Object B because its final temperature is closer to its initial temperature.(D)Thermal energy transfer is still occurring spontaneously from A to B because A was initially hotter.

35. [Skill: 2.C | Topic: 1.4] A sealed container holds $2.0$ moles of a monatomic ideal gas. The gas is heated such that its temperature increases from $300\text{ K}$ to $400\text{ K}$. The ideal gas constant is $R = 8.31\text{ J/(mol}\cdot\text{K)}$. What is the change in the internal energy of the gas during this process? (A) $1662\text{ J}$ (B) $2493\text{ J}$ (C) $4155\text{ J}$ (D) $4986\text{ J}$

(A)(A) $1662\text{ J}$(B)(B) $2493\text{ J}$(C)(C) $4155\text{ J}$(D)(D) $4986\text{ J}$

36. [Skill: 1.1 | Topic: 1.4] [Image Cue]: PV Diagram. The vertical axis is Pressure $P$ and the horizontal axis is Volume $V$. A process is shown as a horizontal line segment starting at point $1$ with coordinates $(V_0, P_0)$ and ending at point $2$ with coordinates $(3V_0, P_0)$. An arrow on the line points from point $1$ to point $2$. A monatomic ideal gas undergoes the thermodynamic process shown in the PV diagram above. Which of the following correctly identifies the work $W$ done ON the gas and the sign of the change in internal energy $\Delta U$ of the gas? (A) $W = -2P_0V_0$ and $\Delta U$ is positive. (B) $W = 2P_0V_0$ and $\Delta U$ is positive. (C) $W = -3P_0V_0$ and $\Delta U$ is negative. (D) $W = -2P_0V_0$ and $\Delta U$ is zero.

(A)(A) $W = -2P_0V_0$ and $\Delta U$ is positive.(B)(B) $W = 2P_0V_0$ and $\Delta U$ is positive.(C)(C) $W = -3P_0V_0$ and $\Delta U$ is negative.(D)(D) $W = -2P_0V_0$ and $\Delta U$ is zero.

37. [Skill: 6.C | Topic: 1.4] A sample of ideal gas is contained in a cylinder with a movable piston. An external force quickly compresses the gas, performing $500\text{ J}$ of work on the system. Simultaneously, the cylinder is in contact with a cold reservoir, and $200\text{ J}$ of energy is transferred out of the gas as heat. What is the change in the internal energy of the gas? (A) $-700\text{ J}$ (B) $-300\text{ J}$ (C) $+300\text{ J}$ (D) $+700\text{ J}$

(A)(A) $-700\text{ J}$(B)(B) $-300\text{ J}$(C)(C) $+300\text{ J}$(D)(D) $+700\text{ J}$

38. [Skill: 2.2 | Topic: 9.5] Two solid spheres, X and Y, have the same mass but are made of different materials. Both spheres are initially at a temperature of $300\text{ K}$. The same amount of thermal energy $Q$ is transferred to each sphere. After the transfer, the final temperature of sphere X is $320\text{ K}$ and the final temperature of sphere Y is $340\text{ K}$. What is the ratio of the specific heat of sphere X to the specific heat of sphere Y, $\frac{c_X}{c_Y}$?

(A)1/2(B)1(C)2(D)4

39. [Skill: 1.4 | Topic: 9.5] A student is investigating the rate of heat conduction through a rectangular metal bar of length $L$, cross-sectional area $A$, and thermal conductivity $k$. The bar connects a steam bath at $100^\circ\text{C}$ and an ice bath at $0^\circ\text{C}$. The student then replaces the bar with a new bar of the same material that has twice the length ($2L$) and twice the cross-sectional area ($2A$). How does the new rate of heat transfer $H_{new}$ compare to the original rate $H_{old}$?

(A)H_{new} = $\frac{1}{4} $H_{old}(B)H_{new} = $\frac{1}{2} $H_{old}(C)H_{new} = H_{old}(D)H_{new} = 2 H_{old}

40. [Skill: 5.1 | Topic: 9.5] A laboratory experiment measures the rate of heat transfer $P = \frac{Q}{\Delta t}$ through various samples of Material 1 and Material 2. The samples have different cross-sectional areas $A$ and lengths $L$, but all experiments are conducted with the same temperature difference $\Delta T$ across the samples. A graph is plotted showing $P$ as a function of the geometric factor $\frac{A}{L}$. [Image Cue]: [Line graph], [Heat Transfer Rate vs. Geometric Factor], [X-axis: A/L (m), Y-axis: P (W)], [Two linear trends starting from the origin. Line 1 (representing Material 1) has a steeper slope than Line 2 (representing Material 2)]. Which of the following statements is correctly supported by the graph and the principles of thermal conduction?

(A)Material 1 has a higher thermal conductivity than Material 2 because the slope of the $P$ vs. $A/L$ graph is proportional to $k$.(B)Material 2 has a higher thermal conductivity than Material 1 because it requires a larger geometric factor to achieve the same power.(C)The thermal conductivity of both materials is the same because both graphs are linear, showing that $k$ is constant for each material.(D)The specific heat of Material 1 must be greater than Material 2 because it transfers energy more efficiently.

41. [Skill: 1.4 | Topic: 1.6] A block of hot metal at temperature $T_H$ is placed inside a thermally insulated container filled with cold water at temperature $T_C$. The metal and water are allowed to reach thermal equilibrium at a final temperature $T_F$. Which of the following best describes the change in entropy of the metal-water system during this process?

(A)The total entropy of the system remains constant because the container is thermally insulated from the environment.(B)The total entropy of the system increases because the process of heat transfer from a hot object to a cold object is irreversible.(C)The entropy of the water increases by the exact same amount that the entropy of the metal decreases, resulting in no net change.(D)The total entropy of the system decreases because the particles in the metal and water reach a more uniform, ordered state of equilibrium.

42. [Skill: 7.1 | Topic: 1.6] A rigid, thermally insulated tank is divided into two equal halves by a thin, breakable membrane. One half of the tank contains an ideal gas at pressure $P_0$, and the other half is a vacuum. The membrane is suddenly ruptured, allowing the gas to expand and fill the entire tank. Which of the following correctly describes the entropy change of the gas and provides a correct justification?

(A)The entropy remains constant because the tank is insulated ($Q = 0$) and the gas does no work ($W = 0$) expanding into a vacuum.(B)The entropy increases because the gas molecules occupy a larger volume, resulting in a more dispersed distribution of energy.(C)The entropy decreases because the pressure of the gas drops, which reduces the number of collisions between particles.(D)The entropy increases because the internal energy of the gas increases as it expands to fill the additional space.

43. [Skill: 6.4 | Topic: 1.6] An inventor claims to have developed a cyclic heat engine that operates between a hot reservoir at $600\text{ K}$ and a cold reservoir at $300\text{ K}$. The engine absorbs $1000\text{ J}$ of thermal energy from the hot reservoir and performs $1000\text{ J}$ of mechanical work. Which of the following statements best evaluates this claim based on the laws of thermodynamics?

(A)The claim is consistent with both the first and second laws of thermodynamics because energy is conserved and the engine is cyclic.(B)The claim violates the first law of thermodynamics because the work done cannot exceed the heat absorbed.(C)The claim violates the second law of thermodynamics because it is impossible to convert all absorbed heat into work in a cyclic process without exhausting some heat to a cold reservoir.(D)The claim is consistent with the second law of thermodynamics because the entropy of the hot reservoir decreases while the work is being performed.

44. [Skill: 1.4 | Topic: 1.1] A rigid, sealed container holds an ideal gas at a constant temperature $T$. A student observes that if more of the same gas is injected into the container while maintaining the same temperature, the measured pressure $P$ increases. Which of the following best explains this observation at the microscopic level?

(A)The average force exerted by each individual atom during a single collision with the wall increases because the atoms are moving faster.(B)The number of atomic collisions with the container walls per unit time increases, resulting in a greater total force exerted on the surface area.(C)The atoms collide with each other more frequently, which increases the average kinetic energy of the system and thus the pressure.(D)The atoms become more densely packed, which increases the perpendicular component of the force exerted by each individual atom upon impact.

45. [Skill: 2.2 | Topic: 1.1] Two separate containers, $X$ and $Y$, are filled with different ideal gases. Container $X$ contains helium gas (atomic mass $4u$) and Container $Y$ contains neon gas (atomic mass $20u$). Both gases are at the same temperature $T$. Which of the following correctly compares the average kinetic energy $K_{avg}$ and the root-mean-square speed $v_{rms}$ of the atoms in the two containers?

(A)The $K_{avg}$ of the helium atoms is equal to the $K_{avg}$ of the neon atoms, but the $v_{rms}$ of the helium atoms is greater than that of the neon atoms.(B)The $K_{avg}$ of the helium atoms is less than the $K_{avg}$ of the neon atoms, but their $v_{rms}$ values are equal.(C)The $K_{avg}$ of the helium atoms is equal to the $K_{avg}$ of the neon atoms, and the $v_{rms}$ of the helium atoms is equal to that of the neon atoms.(D)The $K_{avg}$ of the helium atoms is greater than the $K_{avg}$ of the neon atoms, and the $v_{rms}$ of the helium atoms is greater than that of the neon atoms.

46. [Skill: 6.4 | Topic: 1.1] A sample of an ideal gas is contained in a cube of volume $V$. The temperature of the gas is increased from $T$ to $4T$. Which of the following statements correctly describes the resulting change in the pressure exerted by the gas and provides the correct microscopic justification?

(A)The pressure doubles because the average speed of the atoms doubles, leading to twice as much momentum transfer per collision.(B)The pressure quadruples because the average kinetic energy quadruples, which quadruples the force exerted by each atom during a collision.(C)The pressure quadruples because the average speed of the atoms doubles, which doubles both the momentum change per collision and the frequency of collisions with the walls.(D)The pressure remains the same because the increase in atomic speed is offset by the increase in the time interval between collisions with the container walls.

47. [Skill: 1.1 | Topic: 1.2] A sample of an ideal gas is contained in a rigid tank at a constant temperature. According to the kinetic molecular theory and the classical model of an ideal gas, which of the following statements best describes the interactions between the atoms of the gas?

(A)The atoms exert significant attractive forces on each other except during the brief moments of collision.(B)The atoms move in predictable, non-random paths determined by their initial positions.(C)The only significant forces exerted on the atoms occur during elastic collisions with other atoms or the container walls.(D)A portion of the total kinetic energy is lost as heat every time two atoms collide with one another.

48. [Skill: 5.1 | Topic: 1.2] A student conducts an experiment to measure the pressure of a fixed number of moles of an ideal gas in a sealed container of fixed volume as the temperature is varied. The student plots the pressure $P$ as a function of temperature $T$ in degrees Celsius, as shown in the graph below. Which of the following describes the correct procedure to determine the value of absolute zero from this graph? [Image Cue]: Line graph, Pressure vs. Temperature (Celsius). The y-axis is Pressure $P$, the x-axis is Temperature $T$ in $^{\circ}C$. A linear set of data points shows pressure increasing with temperature. A dashed line extends the linear fit backward toward the x-axis.

(A)Identify the y-intercept of the graph, which represents the pressure at $0^{\circ}C$.(B)Extrapolate the linear fit of the data to the point where the pressure $P$ is zero; the corresponding temperature is absolute zero.(C)Calculate the slope of the line, which is equal to the value of absolute zero in Kelvin.(D)Find the temperature at which the pressure is $1.0 \text{ atm}$, as this is the definition of the absolute temperature scale.

49. [Skill: 2.2 | Topic: 1.2] A cylinder with a frictionless movable piston contains $n$ moles of an ideal gas. Initially, the gas has a pressure $P_0$, a volume $V_0$, and an absolute temperature $T_0$. The gas undergoes a process where the piston is moved to decrease the volume to $\frac{1}{3}V_0$ while the absolute temperature is simultaneously increased to $2T_0$. What is the new pressure $P_f$ of the gas in terms of $P_0$?

(A)$\frac{2}{3}$P_0(B)$\frac{3}{2}$P_0(C)5P_0(D)6P_0

50. [Skill: 6.4 | Topic: 1.3] Two identical metal spheres, Sphere 1 and Sphere 2, are placed in an electrically and thermally insulated container. Initially, Sphere 1 is at a temperature of $T_1 = 450\text{ K}$ and Sphere 2 is at a temperature of $T_2 = 300\text{ K}$. The spheres are brought into physical contact. Which of the following best describes the state of the system after a long period of time has passed?

(A)Energy has stopped flowing between the spheres because Sphere 1 has exhausted its thermal energy.(B)The spheres have reached thermal equilibrium, and there is no net transfer of energy between them.(C)Energy continues to flow spontaneously from Sphere 1 to Sphere 2 because Sphere 1 was initially hotter.(D)The total energy of the system has decreased because energy was lost during the transfer process between the spheres.

51. [Skill: 1.4 | Topic: 1.3] A student is investigating the rate of energy transfer through three different rods of identical length and cross-sectional area. The rods are made of aluminum, glass, and wood. One end of each rod is placed in boiling water ($100^\circ\text{C}$) and the other end is in contact with an ice-water bath ($0^\circ\text{C}$). The student observes that the ice in the bath in contact with the aluminum rod melts significantly faster than the ice in the other two baths. Which of the following statements best explains this observation based on thermal processes?

(A)The aluminum rod has a higher heat capacity, allowing it to store more energy to melt the ice.(B)Convection currents within the aluminum rod move energy more efficiently than in the glass or wood rods.(C)The aluminum rod is a better thermal conductor, resulting in a higher rate of energy transfer via conduction.(D)Radiation from the boiling water travels through the aluminum rod more easily than through the glass or wood.

52. [Skill: 6.2 | Topic: 1.3] A hot ceramic coffee mug is placed inside a vacuum chamber where all air has been evacuated. The walls of the vacuum chamber are maintained at a constant room temperature ($20^\circ\text{C}$). Which of the following correctly predicts the behavior of the mug and provides the correct justification?

(A)The mug will not cool down because there are no air molecules to carry energy away via conduction or convection.(B)The mug will cool down until it reaches $0\text{ K}$ because the vacuum acts as a perfect heat sink.(C)The mug will eventually reach $20^\circ\text{C}$ because it will transfer energy to the chamber walls via radiation.(D)The mug will reach thermal equilibrium with the vacuum itself, which has a temperature of $0\text{ K}$.

53. [Skill: 6.C | Topic: 1.4] A cylinder with a fixed volume contains $2.0\text{ mol}$ of an ideal monatomic gas at an initial temperature of $300\text{ K}$. The gas is heated until its temperature reaches $900\text{ K}$. Which of the following is the best estimate for the change in the internal energy $\Delta U$ of the gas system? (A) $\frac{3}{2}nR(300\text{ K})$ (B) $\frac{3}{2}nR(600\text{ K})$ (C) $\frac{3}{2}nR(900\text{ K})$ (D) $0\text{ J}$, because the volume of the container is fixed and no work is done.

(A)$\frac{3}{2}nR(300\text{ K})$(B)$\frac{3}{2}nR(600\text{ K})$(C)$\frac{3}{2}nR(900\text{ K})$(D)0 J, because the volume of the container is fixed and no work is done.

54. [Skill: 2.B | Topic: 1.4] A sample of ideal gas is taken through the process $A \rightarrow B$ shown in the $PV$ diagram. During this process, $500\text{ J}$ of energy is transferred into the gas via heating ($Q = +500\text{ J}$). What is the change in the internal energy $\Delta U$ of the gas? [Image Cue]: PV diagram. The vertical axis is Pressure $P$ in pascals ($\text{Pa}$) and the horizontal axis is Volume $V$ in cubic meters ($\text{m}^3$). A horizontal line segment starts at point A $(1.0 \times 10^{-3}, 2.0 \times 10^5)$ and ends at point B $(3.0 \times 10^{-3}, 2.0 \times 10^5)$. (A) $100\text{ J}$ (B) $400\text{ J}$ (C) $500\text{ J}$ (D) $900\text{ J}$

(A)100 J(B)400 J(C)500 J(D)900 J

55. [Skill: 1.4 | Topic: 1.4] An ideal gas is contained in a cylinder with a movable piston. An external force compresses the gas so slowly that the temperature of the gas remains constant. Which of the following correctly describes the signs of the heat $Q$ transferred to the gas, the work $W$ done on the gas, and the change in internal energy $\Delta U$ of the gas? (A) $Q > 0$, $W > 0$, $\Delta U > 0$ (B) $Q < 0$, $W > 0$, $\Delta U = 0$ (C) $Q = 0$, $W > 0$, $\Delta U > 0$ (D) $Q < 0$, $W < 0$, $\Delta U = 0$

(A)Q > 0, W > 0, ΔU > 0(B)Q < 0, W > 0, ΔU = 0(C)Q = 0, W > 0, ΔU > 0(D)Q < 0, W < 0, ΔU = 0

56. [Skill: 2.D | Topic: 1.5] A cylindrical metal rod of length $L$ and radius $R$ is used to conduct energy between two heat reservoirs at temperatures $T_H$ and $T_C$, where $T_H > T_C$. The steady-state rate of heat transfer through the rod is $P$. If the rod is replaced by a second rod made of the same material but with length $2L$ and radius $2R$, what is the new rate of heat transfer $P'$ in terms of $P$?

(A)$P/2$(B)$P$(C)$2P$(D)$4P$

57. [Skill: 6.C | Topic: 1.5] A student places one end of a copper rod and one end of a glass rod of identical dimensions into a container of boiling water. The student holds the other ends with their bare hands. The student quickly notices that the copper rod becomes uncomfortably hot to the touch, while the glass rod remains relatively cool for a much longer duration. Which of the following provides the best microscopic justification for this observation?

(A)Copper has a lower density than glass, so thermal energy moves faster through the less dense medium.(B)The specific heat of copper is lower than that of glass, meaning it requires less energy to reach a high temperature.(C)Copper has a higher thermal conductivity because its metallic bonding provides a 'sea' of mobile electrons that efficiently transfer kinetic energy through the lattice.(D)Glass is an amorphous solid, which means its atoms are arranged randomly, preventing any vibration from being passed from one atom to the next.

58. [Skill: 6.C | Topic: 1.6] A hot metal block is placed inside a thermally insulated container filled with cool water. The block and water are allowed to reach thermal equilibrium. Which of the following correctly describes the change in entropy of the metal block and the change in the total entropy of the block-water system? (A) Entropy of the block: Increases; Total entropy of the system: Increases (B) Entropy of the block: Decreases; Total entropy of the system: Increases (C) Entropy of the block: Decreases; Total entropy of the system: Remains the same (D) Entropy of the block: Increases; Total entropy of the system: Remains the same

(A)Entropy of the block: Increases; Total entropy of the system: Increases(B)Entropy of the block: Decreases; Total entropy of the system: Increases(C)Entropy of the block: Decreases; Total entropy of the system: Remains the same(D)Entropy of the block: Increases; Total entropy of the system: Remains the same

59. [Skill: 7.B | Topic: 1.6] A heat engine operates by taking energy $Q_H$ from a high-temperature reservoir, performing work $W$, and exhausting energy $Q_C$ to a low-temperature reservoir. Which of the following best explains why it is impossible for the engine to convert all of the input energy $Q_H$ into work $W$? (A) The first law of thermodynamics requires that some energy be lost to friction in the mechanical parts of the engine. (B) The second law of thermodynamics requires that the total entropy of the universe increase, which necessitates the dispersal of some energy to the cold reservoir. (C) The closed system of the engine must conserve its internal energy, so the heat exhausted must equal the heat absorbed. (D) Energy dispersal is only relevant for isolated systems, and since the engine is a closed system, it must maintain a constant entropy.

(A)The first law of thermodynamics requires that some energy be lost to friction in the mechanical parts of the engine.(B)The second law of thermodynamics requires that the total entropy of the universe increase, which necessitates the dispersal of some energy to the cold reservoir.(C)The closed system of the engine must conserve its internal energy, so the heat exhausted must equal the heat absorbed.(D)Energy dispersal is only relevant for isolated systems, and since the engine is a closed system, it must maintain a constant entropy.

60. [Skill: 1.4 | Topic: 1.6] An ideal gas is held in a cylinder with a movable piston. The cylinder is placed in a large water bath held at a constant temperature. An external force slowly pushes the piston down, compressing the gas isothermally. Which of the following statements correctly describes the entropy of the gas and the justification for its change? (A) The entropy of the gas increases because the external force does work on the system, adding energy to the particles. (B) The entropy of the gas remains constant because the temperature of the gas does not change during an isothermal process. (C) The entropy of the gas decreases because the gas is a closed system and heat energy is transferred from the gas to the water bath. (D) The entropy of the gas must increase because the second law of thermodynamics states that the entropy of any system cannot decrease over time.

(A)The entropy of the gas increases because the external force does work on the system, adding energy to the particles.(B)The entropy of the gas remains constant because the temperature of the gas does not change during an isothermal process.(C)The entropy of the gas decreases because the gas is a closed system and heat energy is transferred from the gas to the water bath.(D)The entropy of the gas must increase because the second law of thermodynamics states that the entropy of any system cannot decrease over time.

61. [Skill: 1.4 | Topic: 1.1] Container 1 contains Helium gas (atomic mass $4u$) and Container 2 contains Neon gas (atomic mass $20u$). Both containers are at the same temperature $T$ and have the same volume. Which of the following correctly compares the average kinetic energy $K_{avg}$ and the root-mean-square speed $v_{rms}$ of the atoms in the two containers?

(A)$K_{avg}$ is the same for both gases, and $v_{rms}$ is the same for both gases.(B)$K_{avg}$ is the same for both gases, but $v_{rms}$ is greater for the Helium atoms.(C)$K_{avg}$ is greater for the Neon atoms, but $v_{rms}$ is greater for the Helium atoms.(D)$K_{avg}$ is greater for the Neon atoms, and $v_{rms}$ is the same for both gases.

62. [Skill: 1.1 | Topic: 1.2] A physics student is using a computer simulation to model the behavior of a gas. To simplify the calculations, the simulation assumes that the particles have no volume and that there are no attractive or repulsive forces between the particles except during collisions. Which of the following statements best justifies why this model is considered an "ideal gas"? (A) The particles will lose kinetic energy over time due to collisions with the walls. (B) The pressure exerted by the gas is solely due to the collisions of particles with the container walls. (C) The temperature of the gas is independent of the average kinetic energy of the particles. (D) The total volume of the gas is significantly smaller than the volume of the individual particles.

(A)The particles will lose kinetic energy over time due to collisions with the walls.(B)The pressure exerted by the gas is solely due to the collisions of particles with the container walls.(C)The temperature of the gas is independent of the average kinetic energy of the particles.(D)The total volume of the gas is significantly smaller than the volume of the individual particles.

63. [Skill: 1.4 | Topic: 1.2] Two identical canisters, $1$ and $2$, contain the same number of moles of an ideal gas. Canister $1$ has a volume $V_1$ and is kept at an absolute temperature $T_1$. Canister $2$ has a volume $V_2 = 2V_1$ and is kept at an absolute temperature $T_2 = 0.5T_1$. If the pressure in canister $1$ is $P_1$, which of the following is the correct expression for the pressure $P_2$ in canister $2$? (A) $0.25 P_1$ (B) $0.5 P_1$ (C) $P_1$ (D) $4 P_1$

(A)0.25 P_1(B)0.5 P_1(C)P_1(D)4 P_1

64. [Skill: 6.4 | Topic: 1.3] A small metal sphere at $T = 500\text{ K}$ is suspended by a thin non-conducting string inside a large vacuum chamber. The walls of the vacuum chamber are maintained at a constant temperature of $T = 293\text{ K}$. Which of the following statements correctly justifies the mechanism of energy transfer and the eventual state of the sphere? (A) The sphere will not cool down because conduction and convection require a medium, which is absent in a vacuum. (B) The sphere will reach thermal equilibrium with the chamber walls primarily through radiation, at which point the net energy exchange is zero. (C) The sphere will transfer energy to the chamber walls through convection as the residual air molecules in the 'vacuum' carry heat away. (D) The sphere will reach thermal equilibrium when its temperature is lower than the wall temperature, as energy is lost to the surroundings.

(A)The sphere will not cool down because conduction and convection require a medium, which is absent in a vacuum.(B)The sphere will reach thermal equilibrium with the chamber walls primarily through radiation, at which point the net energy exchange is zero.(C)The sphere will transfer energy to the chamber walls through convection as the residual air molecules in the 'vacuum' carry heat away.(D)The sphere will reach thermal equilibrium when its temperature is lower than the wall temperature, as energy is lost to the surroundings.

65. [Skill: 1.1 | Topic: 1.3] An experimenter places a $1.0\text{ kg}$ block of aluminum ($T = 350\text{ K}$) and a $5.0\text{ kg}$ block of copper ($T = 350\text{ K}$) into a thermal reservoir. Which of the following best describes the state of the two blocks relative to each other? (A) Energy will flow from the copper block to the aluminum block because the copper block has more mass and thus more internal energy. (B) Energy will flow from the aluminum block to the copper block because aluminum has a higher specific heat capacity. (C) The blocks are in thermal equilibrium with each other because they are at the same temperature, meaning there is no net energy transfer between them. (D) Energy will flow between the blocks until the total internal energy of the system is minimized.

(A)Energy will flow from the copper block to the aluminum block because the copper block has more mass and thus more internal energy.(B)Energy will flow from the aluminum block to the copper block because aluminum has a higher specific heat capacity.(C)The blocks are in thermal equilibrium with each other because they are at the same temperature, meaning there is no net energy transfer between them.(D)Energy will flow between the blocks until the total internal energy of the system is minimized.

66. [Skill: 7.1 | Topic: 1.4] A rigid, sealed container contains a fixed amount of an ideal monatomic gas. If the absolute temperature of the gas is doubled, which of the following best describes the change in the internal energy of the system and provides the correct microscopic justification?

(A)The internal energy doubles because the average kinetic energy of the gas atoms doubles.(B)The internal energy doubles because the potential energy of the interaction between atoms doubles.(C)The internal energy increases by a factor of four because the root-mean-square speed of the atoms doubles.(D)The internal energy remains unchanged because the volume of the rigid container is constant, so no work is done.

67. [Skill: 2.2 | Topic: 1.5] A cylindrical metal rod of length $L$ and cross-sectional area $A$ connects two thermal reservoirs at temperatures $T_H = 100^\circ C$ and $T_C = 0^\circ C$. The rate of energy transfer by conduction through this rod is $H_1$. A second rod is made of the same metal but has a length $2L$ and a radius that is twice the radius of the first rod. This second rod is placed between the same two reservoirs. What is the rate of energy transfer $H_2$ through the second rod in terms of $H_1$?

(A)$H_2 = 0.5 H_1$(B)$H_2 = H_1$(C)$H_2 = 2 H_1$(D)$H_2 = 4 H_1$

68. [Skill: 6.4 | Topic: 1.5] A student holds one end of a copper rod and one end of a wooden rod of identical dimensions. The other ends of both rods are placed in a container of boiling water. The student notes that the copper rod becomes uncomfortably hot to hold within seconds, while the wooden rod remains cool for several minutes. Which of the following best explains this observation based on the properties of the materials?

(A)Copper has a higher specific heat than wood, allowing it to store more thermal energy.(B)The thermal conductivity of copper is an intrinsic property determined by its atomic structure and the presence of free electrons, which facilitates faster energy transfer.(C)The wood is more dense than the copper, which prevents the vibrations of atoms from traveling through the material effectively.(D)The rate of energy transfer is higher in copper because the temperature difference across the copper rod is greater than the temperature difference across the wooden rod.

69. [Skill: 6.4 | Topic: 1.6] A thermally insulated container is divided into two equal volumes by a thin, removable partition. Side A contains an ideal gas at a high temperature $T_H$, and Side B contains the same amount of the same gas at a lower temperature $T_C$. The partition is removed, and the system is allowed to reach thermal equilibrium. Which of the following statements correctly describes the change in entropy for the system?

(A)The entropy of the gas in Side A increases, while the entropy of the gas in Side B decreases.(B)The entropy of the gas in Side A decreases, while the entropy of the gas in Side B increases, resulting in a net increase in the total entropy of the system.(C)The total entropy of the system remains constant because the container is thermally insulated and no heat enters from the environment.(D)The total entropy of the system decreases because the temperature gradient is eliminated, leading to a more ordered state.

70. [Skill: 6.4 | Topic: 1.6] An engineer is designing a heat engine that absorbs $Q_H$ from a hot reservoir and performs work $W$. Which of the following best explains why the engine must exhaust some amount of heat $Q_C$ to a cold reservoir, making it impossible to achieve $100\%$ efficiency?

(A)The First Law of Thermodynamics requires that energy be conserved, so $Q_H$ must be split between work and exhaust.(B)Friction in the mechanical parts of the engine inevitably converts some work into thermal energy.(C)Converting all heat $Q_H$ into work $W$ would result in a net decrease in the entropy of the universe.(D)The exhaust heat is necessary to increase the internal energy of the cold reservoir to maintain the temperature gradient.

71. [Skill: 7.2 | Topic: 1.6] A sample of liquid water is placed inside a freezer. As the water turns into ice, its entropy decreases. Which of the following statements correctly justifies why this process does not violate the Second Law of Thermodynamics?

(A)The Second Law only applies to isolated systems; the water is a closed system that transfers energy to its surroundings.(B)The entropy of the water molecules increases during a phase change from liquid to solid because the molecules are locked in place.(C)The work done by the freezer's motor creates an equal and opposite change in the water's entropy.(D)Phase changes are considered reversible processes, and the Second Law states that entropy is constant for all reversible processes.

72. [Skill: 1.4 | Topic: 1.1] A rigid, sealed container holds a sample of an ideal gas at an initial absolute temperature $T$. The gas particles have a root-mean-square speed $v_{rms}$ and exert a pressure $P$ on the walls of the container. If the temperature of the gas is increased to $4T$, which of the following identifies the new root-mean-square speed of the particles and the new pressure exerted by the gas? (A) The new speed is $2v_{rms}$ and the new pressure is $4P$. (B) The new speed is $4v_{rms}$ and the new pressure is $4P$. (C) The new speed is $2v_{rms}$ and the new pressure is $2P$. (D) The new speed is $16v_{rms}$ and the new pressure is $4P$.

(A)The new speed is $2v_{rms}$ and the new pressure is $4P$.(B)The new speed is $4v_{rms}$ and the new pressure is $4P$.(C)The new speed is $2v_{rms}$ and the new pressure is $2P$.(D)The new speed is $16v_{rms}$ and the new pressure is $4P$.

73. [Skill: 2.B | Topic: 1.5] Two cylindrical rods, Rod $X$ and Rod $Y$, are made of the same metallic alloy. Rod $X$ has a length $L$ and a radius $r$. Rod $Y$ has a length $2L$ and a radius $2r$. Both rods are used to connect two thermal reservoirs, one at temperature $T_H$ and the other at temperature $T_C$, where $T_H > T_C$. If the rate of energy transfer by conduction through Rod $X$ is $P_X$, which of the following correctly expresses the rate of energy transfer by conduction through Rod $Y$, $P_Y$, in terms of $P_X$?

(A)$P_Y = \frac{1}{2} P_X$(B)$P_Y = P_X$(C)$P_Y = 2 P_X$(D)$P_Y = 4 P_X$

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