MCAT Physics and Math Review

Chapter 3: Thermodynamics

Practice Questions

1.    If an object with an initial temperature of 300 K increases its temperature by 1°C every minute, by how many degrees Fahrenheit will its temperature have increased in 10 minutes?

1.    6°F

2.    10°F

3.    18°F

4.    30°C

2.    Which of the following choices correctly identifies the following three heat transfer processes?

1.    Heat transferred from the Sun to the Earth

2.    A metal spoon heating up when placed in a pot of hot soup

3.    A rising plume of smoke from a fire

1.    I. Radiation; II. Conduction; III. Convection

2.    I. Conduction; II. Radiation; III. Convection

3.    I. Radiation; II. Convection; III. Conduction

4.    I. Convection; II. Conduction; III. Radiation

3.    A 20 m steel rod at 10°C is dangling from the edge of a building and is 2.5 cm from the ground. If the rod is heated to 90°C, will the rod touch the ground? (Note: α = 1.1 × 10−5 K−1)

1.    Yes, because it expands by 3.2 cm.

2.    Yes, because it expands by 2.6 cm.

3.    No, because it expands by 2.2 cm.

4.    No, because it expands by 1.8 cm.

4.    What is the final temperature of a 5 kg silver pendant that is left in front of an electric heater, absorbing heat energy at a rate of 100 W for 10 minutes? Assume the pendant is initially at 20°C and that the specific heat of silver is 

1.    29°C

2.    59°C

3.    72°C

4.    100°C

5.    How much heat is required to completely melt 500 g gold earrings, given that their initial temperature is 25°C? (The melting point of gold is 1064°C, its heat of fusion is  and its specific heat is 

1.    15 kJ

2.    32 kJ

3.    66 kJ

4.    97 kJ

6.    Given the cycle shown, what is the total work done by the gas during the cycle?

1.    –10 J

2.    0 J

3.    7.5 J

4.    17.5 J

7.    In an adiabatic compression process, the internal energy of the gas:

1.    increases because the work done on the gas is negative.

2.    increases because the work done on the gas is positive.

3.    decreases because the work done on the gas is negative.

4.    decreases because the work done on the gas is positive.

8.    The entropy of a system can:

1.    never decrease.

2.    decrease when the entropy of the surroundings increases by at least as much.

3.    decrease when the system is isolated and the process is irreversible.

4.    decrease during an adiabatic reversible process.

9.    A student making a coffee cup calorimeter fails to use a second coffee cup and incompletely seals the lid. What was her initial goal, and what was the result of this mistake?

1.    She was trying to create an isolated system but created an open system instead.

2.    She was trying to create an isolated system but created a closed system instead.

3.    She was trying to create a closed system but created an open system instead.

4.    She was trying to create a closed system but created an isolated system instead.

10.A certain substance has a specific heat of  and a melting point of 350 K. If one mole of the substance is currently at a temperature of 349 K, how much energy must be added in order to melt it?

1.    More than 1 J

2.    Exactly 1 J

3.    Less than 1 J but more than 0 J

4.    Less than 0 J

11.Which of the following is NOT a state function?

1.    Internal energy

2.    Heat

3.    Temperature

4.    Entropy

12.The figure shown depicts a thick metal container with two compartments. Compartment A is full of a hot gas, while compartment B is full of a cold gas. What is the primary mode of heat transfer in this system?

1.    Radiation

2.    Convection

3.    Conduction

4.    Enthalpy

13.Substances A and B have the same freezing and boiling points. If solid samples of both substances are heated in the exact same way, substance A boils before substance B. Which of the following would NOT explain this phenomenon?

1.    Substance B has a higher specific heat.

2.    Substance B has a higher heat of vaporization.

3.    Substance B has a higher heat of fusion.

4.    Substance B has a higher internal energy.

14.In experiment A, a student mixes ink with water and notices that the two liquids mix evenly. In experiment B, the student mixes oil with water; in this case, the liquids separate into two different layers. The entropy change is:

1.    positive in experiment A and negative in experiment B.

2.    positive in experiment A and zero in experiment B.

3.    negative in experiment A and positive in experiment B.

4.    zero in experiment A and negative in experiment B.

15.Which of the following processes is LEAST likely to be accompanied by a change in temperature?

1.    The kinetic energy of a gas is increased through a chemical reaction.

2.    Energy is transferred to a solid via electromagnetic waves.

3.    A boiling liquid is heated on a hot plate.

4.    A warm gas is mixed with a cold gas.

PRACTICE QUESTIONS

Answers and Explanations

1.    CThe kelvin unit and Celsius degree are the same size; that is, a change of 10 K is equal to a change of 10°C. One degree Celsius is equal to 1.8 degrees Fahrenheit; therefore, 10°C = 18°F.

2.    ABecause there is essentially only empty space between the Sun and the Earth, the only means of heat transfer is by radiation—electromagnetic waves that propagate across space. When a metal spoon is placed in a pot of hot soup, the molecules in the soup collide with those on the surface of the spoon, thereby transferring heat by conduction. Finally, fire warms the air above it, and the warmed air is less dense than the surrounding air, so it rises. A rising column of warm air means that heat is being transported in the air mass, which is simply the process of convection. The smoke particles ride along with the upward moving air current and create a plume of smoke.

3.    D

First, find the change in length due to thermal expansion:

Because the rod is originally 2.5 cm above the ground and its length increases by 1.76 cm, we can conclude that it will not touch the ground after the thermal expansion process is completed.

4.    C

To answer this question, first remember that watts are equal to joules per second; in other words, power is energy transfer over time. In 10 minutes, the pendant absorbs the following amount of energy:

Now we can find the final temperature from this equation:

The final temperature is thus 20 + 52 = 72°C.

5.    D

First determine how much heat is required to raise the temperature of the gold earrings to the melting point of gold. Then, calculate the heat required to actually melt the earrings (the latent heat). The total heat required to melt the earrings completely will be the sum of the two heats. The heat required to raise the temperature of the earrings from 25°C to 1064°C is

Thus, it takes about 60 kJ of heat to bring the earrings to their melting point. The next step is to calculate how much heat is needed to melt the earrings. For this, use the heat of fusion (the latent heat) of gold:

So overall, it requires approximately 60 + 32 kJ = 92 kJ of heat to melt the gold earrings. Notice that we can heavily approximate the numbers used in our calculations because the answer choices are so spread out. The closest answer is choice (D).

6.    CThe total work done by the cycle is the sum of the work of paths A, B, and C, or the area within the cycle. Because the area bounded by A, B, and C is a triangle with a base of 5 m3 and a height of 3 Pa, we can calculate the area as  Clockwise loops tend to do positive work on the environment, while counterclockwise loops do negative work.

7.    BTo answer the question, make sure you understand all the terms. An adiabatic process means that there is no exchange of heat; in other words, Q = 0. When a gas is compressed, positive work is being done on the gas (rather than by the gas), so the value for work done by the gas will be negative (W < 0). Based on this, we can determine how the internal energy of the gas changes by using the first law of thermodynamics (ΔU = Q − W). If Q = 0 and W is negative, then ΔU is positive.

8.    BThe entropy of a system can decrease as long as the entropy of its surroundings increases by at least as much. On the other hand, the entropy of an isolated system increases for all real (irreversible) processes. This adheres to the second law of thermodynamics, which says that energy will be dispersed and entropy of the universe will remain constant or increase during all processes.

9.    BCalorimeters are our best approximations of isolated systems, where neither energy nor matter is exchanged with the environment. By failing to use an insulating layer and failing to fully contain the system, heat can be exchanged with the environment and pressure may be dissipated. Because the question stem implies that the top was mostly secured, it is reasonable to believe that this now approximates a closed system and not an open system because matter is not exchanged with the environment.

10.ATo find the amount of heat needed to bring the substance to its melting point, you can use the specific heat. To heat one mole of the substance one unit kelvin, it would take 1 J of heat. After the substance reaches its melting point, additional heat is needed to actually induce the phase change. Therefore, the total amount of heat required is greater than 1 J.

11.BState functions are any which are independent of path taken to achieve a given state and which are not themselves defined as a process, such as pressure, density, temperature, volume, enthalpy, internal energy, Gibbs free energy, and entropy. Heat and work are process functions that are pathway-dependent.

12.CIn this situation, heat will transfer from the warm gas to the metal and then to the cold gas. Choice (B), convection, requires flow of a fluid to cause heat transfer. In this case, the gas is not flowing, but rather is in contact with the metal. Choice (A), heat transfer through radiation, is also implausible not only because gases are unlikely to emit heat in the form of waves, but also because the radiation would be unlikely to penetrate the thick metal container. Enthalpy, choice (D), is not a form of heat transfer. Conduction, choice (C), is the most likely option; it happens when two substances make direct contact with one another. Here, gas A makes contact with the metal container, which makes contact with gas B.

13.DSaying that substance B has a higher internal energy cannot explain the phenomenon because the internal energy is irrelevant; the heat involved in the process is related only to the specific heat, the heat of fusion, and the heat of vaporization. All of the other choices could explain the phenomenon. The heat required to melt the solid is determined by the heat of fusion, choice (C). The heat required to bring the liquid to its boiling point is determined by the specific heat, choice (A). The heat required to boil the liquid is determined by the heat of vaporization,choice (B).

14.BWhen the ink randomly intersperses throughout the water, the final state is more disordered than the initial state, so the entropy change of the system is positive. When the oil separates from the water, the final state is just as ordered as the initial state (because the oil and the water are still completely separate), so the entropy change is zero. You can also answer this question by noticing the reversibility of the two experiments. Experiment A has a positive entropy change because it is irreversible, while experiment B has no entropy change because the reaction is reversible. According to the second law of thermodynamics, the overall entropy change can never be negative in a thermodynamic process that moves from one equilibrium state to another.

15.CIf a substance is undergoing a phase change, any added heat will be used toward overcoming the heat of transformation of the phase change. During the phase change, the temperature will remain constant. Temperature is a measure of the kinetic energy of the molecules in a sample, so a change in kinetic energy, choice (A), is essentially the same thing as a change in temperature. The heat transfer by radiation described in choice (B) will definitely change the temperature of the solid as long as it is not in the process of melting. Choice (D) describes heat transfer by convection, in which the warm gas will transfer heat to the cold gas until they both reach an intermediate temperature.