AP Physics 2 - Unit 9 practice questions

Question 1

A sample of an ideal gas is contained in a cylinder with a movable piston. The gas is initially at pressure $P_0$, volume $V_0$, and absolute temperature $T_0$. The gas undergoes a process during which the volume is increased to $2V_0$ and the absolute temperature is decreased to $\frac{1}{2}T_0$. What is the final pressure of the gas?

Accepted Answer

$\frac{1}{4} P_0$

Answer

$\frac{1}{2} P_0$

Answer

$P_0$

Answer

$4 P_0$

Question 2

An ideal gas undergoes a cyclic thermodynamic process represented by the rectangular path $1 \rightarrow 2 \rightarrow 3 \rightarrow 4 \rightarrow 1$ on the pressure-volume ($P\text{-}V$) diagram shown. Which of the following correctly describes the net work done BY the gas and the net change in internal energy of the gas during one complete cycle?

Accepted Answer

The net work done by the gas is positive, and the net change in internal energy is zero.

Answer

The net work done by the gas is zero, and the net change in internal energy is zero.

Answer

The net work done by the gas is positive, and the net change in internal energy is positive.

Answer

The net work done by the gas is negative, and the net change in internal energy is zero.

Question 3

A warm rock at initial temperature $T_h$ is dropped into a large, cool lake at temperature $T_c$, where $T_h > T_c$. Heat transfers spontaneously from the rock to the lake water until the rock reaches thermal equilibrium with the lake. What are the signs of the entropy change of the rock, $\Delta S_{\text{rock}}$, and the total entropy change of the universe, $\Delta S_{\text{univ}}$, for this process?

Accepted Answer

$\Delta S_{\text{rock}} < 0$ and $\Delta S_{\text{univ}} > 0$

Answer

$\Delta S_{\text{rock}} > 0$ and $\Delta S_{\text{univ}} > 0$

Answer

$\Delta S_{\text{rock}} < 0$ and $\Delta S_{\text{univ}} = 0$

Answer

$\Delta S_{\text{rock}} > 0$ and $\Delta S_{\text{univ}} < 0$

Question 4

A hot copper block at initial temperature $T_b$ is placed into an insulated container filled with cool water at initial temperature $T_w$, where $T_b > T_w$. Thermal energy is exchanged only between the copper block and the water until the system reaches thermal equilibrium at temperature $T_f$. Which of the following correctly describes the direction of net thermal energy transfer and the value of the final equilibrium temperature $T_f$?

Accepted Answer

Direction of net heat transfer: From the copper block to the waterFinal temperature: $T_w < T_f < T_b$

Answer

Direction of net heat transfer: From the water to the copper blockFinal temperature: $T_f > T_b$

Answer

Direction of net heat transfer: From the water to the copper blockFinal temperature: $T_w < T_f < T_b$

Answer

Direction of net heat transfer: From the copper block to the waterFinal temperature: $T_f = T_b$

Question 5

A fixed amount of an ideal gas is sealed inside a rigid container of constant volume. The absolute temperature of the gas is doubled from $T_0$ to $2T_0$. How does the pressure of the gas change, and what is the microscopic explanation for this change?

Accepted Answer

The pressure doubles because the average kinetic energy of the gas molecules doubles, resulting in more frequent collisions with the container walls and a greater momentum change per collision.

Answer

The pressure quadruples because doubling the absolute temperature doubles the average speed of the molecules, which quadruples both the rate and force of wall collisions.

Answer

The pressure doubles because each gas molecule expands to occupy twice its original volume, increasing the contact area during wall impacts.

Answer

The pressure remains unchanged because the volume of the rigid container is fixed, so the rate of molecular collisions with the walls remains constant.

Question 6

Two sealed containers, Container A and Container B, are kept in thermal equilibrium at temperature $T_0$. Container A contains helium gas (molar mass $4 \text{ g/mol}$), and Container B contains argon gas (molar mass $40 \text{ g/mol}$). Which of the following correctly compares the average translational kinetic energy $K_{\text{avg}}$ per atom and the root-mean-square speed $v_{\text{rms}}$ of the helium atoms to those of the argon atoms?

Accepted Answer

$K_{\text{avg, He}} = K_{\text{avg, Ar}}$

Answer

$K_{\text{avg, He}} > K_{\text{avg, Ar}}$

Answer

$K_{\text{avg, He}} > K_{\text{avg, Ar}}$

Question 7

A sample of liquid water at $0\text{ }^\circ\text{C}$ is placed inside a freezer and completely freezes into ice at $0\text{ }^\circ\text{C}$. Which of the following correctly describes the entropy change of the water and the total entropy change of the universe, and provides the correct physical justification?

Accepted Answer

The entropy of the water decreases because its molecules become more ordered, while the total entropy of the universe increases because heat released to the surroundings increases the entropy of the surroundings by a greater magnitude.

Answer

The entropy of the water increases because its temperature remains constant during the phase change, and the total entropy of the universe remains unchanged.

Answer

The entropy of the water decreases, and the total entropy of the universe decreases because energy in the form of heat is removed from the system.

Answer

The entropy of the water increases because the crystalline structure stores potential energy, while the total entropy of the universe increases.

Question 8

A sample of an ideal gas is taken through the cycle $1 \to 2 \to 3 \to 4 \to 1$ as shown in the pressure-volume ($P$-$V$) diagram. What is the net work done by the gas during one complete cycle?

Accepted Answer

$600 \text{ J}$

Answer

$300 \text{ J}$

Answer

$900 \text{ J}$

Answer

$1500 \text{ J}$

Question 9

A sample of an ideal gas in a rigid container has an initial absolute temperature $T_1$. The gas is heated until its absolute temperature increases to $T_2 = 2T_1$. Which of the following correctly pairs the factor by which the average translational kinetic energy per molecule changes and the factor by which the root-mean-square speed of the gas molecules changes?

Accepted Answer

Average kinetic energy: Increases by a factor of $2$ ; RMS speed: Increases by a factor of $\sqrt{2}$

Answer

Average kinetic energy: Increases by a factor of $\sqrt{2}$ ; RMS speed: Increases by a factor of $2$

Answer

Average kinetic energy: Increases by a factor of $2$ ; RMS speed: Increases by a factor of $2$

Answer

Average kinetic energy: Increases by a factor of $4$ ; RMS speed: Increases by a factor of $2$

Question 10

A block of ice at a constant melting temperature of $273\text{ K}$ absorbs a quantity of heat $Q$ from a large surrounding room maintained at a constant temperature of $293\text{ K}$ until the ice completely melts. Which of the following correctly compares the magnitude of the entropy change of the ice, $|\Delta S_{\text{ice}}|$, to the magnitude of the entropy change of the room, $|\Delta S_{\text{room}}|$, and provides a correct explanation?

Accepted Answer

$|\Delta S_{\text{ice}}| > |\Delta S_{\text{room}}|$ because the same quantity of heat $Q$ is transferred at a lower absolute temperature for the ice than for the room.

Answer

$|\Delta S_{\text{ice}}| < |\Delta S_{\text{room}}|$ because the room has a much larger mass and heat capacity than the block of ice.

Answer

$|\Delta S_{\text{ice}}| = |\Delta S_{\text{room}}|$ because energy is conserved, so the magnitude of heat absorbed by the ice equals the magnitude of heat released by the room.

Answer

$|\Delta S_{\text{ice}}| < |\Delta S_{\text{room}}|$ because heat flows spontaneously from the higher-temperature room to the lower-temperature ice.

Question 11

A sample of an ideal gas is held inside a cylinder fitted with a movable piston. The gas is initially at temperature $T_0$ and occupies volume $V_0$. The gas then undergoes a slow isothermal expansion until its volume reaches $2V_0$. Which of the following claims correctly describes the change in the rate of molecular collisions per unit area of the cylinder walls and provides a valid physical justification?

Accepted Answer

The collision rate per unit area decreases to half its initial value, because the number density of the gas molecules is halved while their root-mean-square speed remains constant.

Answer

The collision rate per unit area remains unchanged, because the root-mean-square speed of the gas molecules depends only on temperature.

Answer

The collision rate per unit area decreases to half its initial value, because the root-mean-square speed of the molecules is halved while the number density remains constant.

Answer

The collision rate per unit area decreases to one-fourth of its initial value, because both the number density and the root-mean-square speed of the molecules are halved.

Question 12

A student performs an experiment to determine the specific heat capacity of an unknown metal block. The hot block is placed into an insulated cup containing water at room temperature. The student records the initial temperatures of the block and water as well as the final equilibrium temperature of the mixture, assuming no thermal energy is exchanged with the surrounding environment. If a small amount of thermal energy actually escapes to the surrounding air during the process, how will the experimentally calculated specific heat capacity of the metal compare to its true value, and why?

Accepted Answer

It will be less than the true value, because the measured temperature rise of the water is smaller than expected, causing the thermal energy absorbed by the water to be underestimated relative to the energy released by the metal.

Answer

It will be greater than the true value, because a larger temperature drop of the metal implies that the metal released a greater amount of thermal energy per degree.

Answer

It will be greater than the true value, because a lower final equilibrium temperature increases the calculated quantity of thermal energy absorbed by the water.

Answer

It will be less than the true value, because heat loss to the surroundings reduces the intrinsic specific heat capacity of the water during the experiment.

Question 13

Container 1 holds $1.0 \text{ mol}$ of helium gas (monatomic), and Container 2 holds $1.0 \text{ mol}$ of nitrogen gas (diatomic). Both containers are maintained at the same absolute temperature $T_0$. Which of the following correctly compares the average translational kinetic energy per molecule, $K_{\text{avg}}$, and the total internal energy, $U$, of the gas in Container 1 to the gas in Container 2?

Accepted Answer

$K_{\text{avg}}$ is the same in both containers because temperature determines average translational kinetic energy, but $U$ is smaller in Container 1 because monatomic gas molecules have fewer degrees of freedom than diatomic gas molecules.

Answer

$K_{\text{avg}}$ is greater in Container 1 because helium atoms have less mass and thus higher speed, and $U$ is the same in both containers because internal energy depends only on temperature and number of moles.

Answer

$K_{\text{avg}}$ is the same in both containers because temperature determines average translational kinetic energy, and $U$ is the same in both containers because internal energy depends only on temperature and number of moles.

Answer

$K_{\text{avg}}$ is smaller in Container 1 because monatomic molecules have fewer degrees of freedom, and $U$ is smaller in Container 1 because helium has less molar mass than nitrogen.

Question 14

Three heat engines, 1, 2, and 3, each operate on a Carnot cycle between a hot reservoir at absolute temperature $T_H$ and a cold reservoir at absolute temperature $T_C$. The operating temperatures for each engine are given in the table.

| Engine | Hot Reservoir Temperature $T_H$ | Cold Reservoir Temperature $T_C$ |
|---|---|---|
| 1 | $600 \text{ K}$ | $300 \text{ K}$ |
| 2 | $500 \text{ K}$ | $200 \text{ K}$ |
| 3 | $400 \text{ K}$ | $100 \text{ K}$ |

Which of the following correctly ranks the ideal thermal efficiencies $e_1$, $e_2$, and $e_3$ of the three engines?

Accepted Answer

$e_3 > e_2 > e_1$

Answer

$e_1 > e_2 > e_3$

Answer

$e_1 = e_2 = e_3$

Answer

$e_2 > e_3 > e_1$

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