Thermodynamics for the MCAT: Everything You Need to Know

Learn essential MCAT thermodynamics concepts, including laws of thermodynamics, spontaneity, and equilibrium, plus targeted practice questions and solutions

(Note: This guide is part of our MCAT Physics series.)

Table of Contents

Part 1: Introduction to thermodynamics

Part 2: Heat

a) Heat capacity and specific heat

b) Heat of transformation

c) Heat transfer

d) Thermal expansion

Part 3: The Four Laws of Thermodynamics

a) Zeroth law of thermodynamics

b) First law of thermodynamics

c) Second law of thermodynamics

d) Third law of thermodynamics

Part 4: Thermodynamic Functions, Systems, and Processes

a) Types of functions

b) Types of systems

c) Types of processes

Part 5: High-Yield Terms and Equations

Part 6: Passage-Based Questions and Answers

Part 7: Standalone Questions and Answers

----

Part 1: Introduction to thermodynamics

Thermodynamics is an important topic that you likely learned about in chemistry (or physical chemistry) during your undergraduate years. While it is not an extremely high-yield MCAT subject, it can serve as an important foundation for other topics you'll need to know for the exam.

As you go through this guide on thermodynamics, we've bolded several important terms, and we encourage you to create your own definitions and examples as you move through this resource so that they make the most sense to you. At the end of this guide, there's an MCAT-style thermodynamics practice passage and standalone questions that will both test your thermodynamics knowledge and show you how the AAMC likes to ask questions.

Receive a free MCAT Question of the Day—written by a 528 scorer

Get every last bit of practice in before test day with a free MCAT question delivered straight to your inbox daily.

----

Part 2: Heat

When we talk about thermodynamics, many of the concepts will tie back to an important word: heat. Importantly, heat is not the same as temperature. Let’s take a look at the definitions of each word:

Heat: the transfer of energy based on a temperature difference between two objects

Temperature: a measure of the average energy due to motion of particles in an object (i.e., a cold object has slow-moving particles while a hot object has fast-moving particles)

Figure 1     Heat vs temperature

Now that we’ve defined heat, let’s dive into some of its properties. 

a) Heat capacity and specific heat

Heat capacity is the heat required to raise the temperature of an object by a certain unit of temperature. For example, let’s say our “object” is a chair and we want to raise the temperature by 5 °C. Heat capacity would tell us how much heat we need in order to make that happen. 

The SI units for heat capacity are joules (J) / kelvin (K), and this makes sense if we remember that joules are a unit for energy while kelvins are a unit for temperature. 

Specific heat is very similar to heat capacity but defines the amount of our “object” and how much we want to raise the temperature of that object. We define specific heat as the amount of heat required to raise one gram of an object by one degree Kelvin (or Celsius). If we go back to the chair example, we now don’t care about the entire chair or raising the temperature by 5 °C. Instead, we want to know how much heat we need to raise one gram of the chair by 1 °K.

b) Heat of transformation

Heat of transformation is another important thermodynamic term. To understand heat of transformation, let’s look at an example. Ice is the solid form of water, and the process of converting ice to water requires heat. Similarly, the process of converting water to water vapor (the gaseous form of water) requires heat. These transitions are called phase changes, and they are often represented by a phase change diagram:

Figure 2     A measure of the average energy due to motion of particles in an object A phase-change diagram

The phase-change diagram plots temperature versus energy. As we increase the energy, the temperature increases, and we observe a transition from solids to liquids to gases. On the graph, however, you’ll notice flat points in which an increase in energy doesn’t lead to an increase in temperature.

These flat points are the phase changes that we talked about above. During a phase change, the temperature doesn’t change, and we can describe the points with the following equation:

q = m × L
where q = heat gained or lost from the substance,
m = the mass of the substance,
L = the latent heat, or heat of transformation, of the substance

The heat of transformation is an intrinsic property of a substance that defines the energy needed to generate a phase change. The heat of fusion is the heat of transformation constant for a solid to liquid transformation, and the heat of vaporization is the heat of transformation constant for a liquid to gas transformation.

Since these are properties intrinsic to a substance, they will change based on what substance we are looking at. For example, water and aluminum have different heats of transformation, and you’ll be provided this information by a passage should you need it on the exam. 

c) Heat transfer 

We’ve talked about a few different properties of heat, and now we’ll talk about exactly how heat is transferred from one object to another. Heat transfer can occur in three ways:

1.     Conduction: a direct transfer of heat through contact and without movement of the objects

2.     Convection: a transfer of heat through the motion of a liquid or gas over another object

3.     Radiation: an indirect transfer of heat through electromagnetic waves that does not require the two objects to be in contact 

Figure 3    Different forms of heat transfer. In these diagrams, system a is initially hot, while system b is initially cold (lacks heat).

d) Thermal expansion

A long time ago, researchers made an interesting observation: temperature changes in solid objects can change their length. Solid objects tend to increase in length when they are heated up, and to illustrate this point with an example, let’s look at railroads. Due to thermal expansion, railroads must include “wiggle room” so that the railroads don’t buckle and kink when the sun is out.

The formula for thermal expansion is:

ΔL = α × L × ΔT
where ΔL = change in length,
α = coefficient of linear expansion,
L = length,
ΔT = change in temperature

From the equation, we can see that an increase in temperature causes an increase in length, and a decrease in temperature causes a decrease in length. 

The coefficient of linear expansion is a constant intrinsic to a specific material. As a result, it is not a value you need to memorize and would be given to you on test day. The same equation can be used for volumetric expansion, but length “L” is replaced by volume “V” and the coefficient of linear expansion is replaced by the coefficient of volumetric expansion.

Entropy as Measure of "Disorder" and Relative Entropy for Gas, Liquid, and Crystal States

SAC377 code block

----

Part 3: The four laws of thermodynamics

a) Zeroth law of thermodynamics

The zeroth law of thermodynamics states that when two objects are in thermal equilibrium with a third object, the original two objects are in thermal equilibrium with each other. Let’s look at what this means in a simple diagram: 

Figure 4     The zeroth law of thermodynamics

At thermal equilibrium, the temperatures of the objects will be equal, and there will be no net heat transfers between the three objects.

b) First law of thermodynamics

The first law of thermodynamics is best represented by the following equation:

ΔU = Q − W
where ΔU = change in system's internal energy,
Q = heat added to the system,
W = work done by the system

∆U is proportional to the temperature of an object, so an increase in ∆U means the temperature of an object is increasing. If Q is positive, heat is coming into the system. If W is positive, work is being done by the system on the surroundings.

If ∆U is negative, the temperature of the object is decreasing. If Q is negative, heat is leaving the system. If W is negative, the surroundings are doing work on the system. 

c) Second law of thermodynamics

The second law of thermodynamics states that the total entropy of an isolated system (we’ll define this term in the next section) cannot decrease over time. Before we look at an example, let’s think about entropy. Entropy states that energy becomes spread out over time, and we can think of entropy as a movement towards a disordered state. The greater the entropy, the more disordered the energy.

Let’s now look at an example. Picture a beach as our isolated system. If there is a sandcastle on the beach, is this a state of high or low entropy? The sandcastle is in a state of low entropy because the sand is in a highly ordered state.

If we sat on a beach for a hundred years, would a sandcastle would spontaneously appear? Probably not. According to our second law of thermodynamics, the sand would likely become even more spread out and not form a well-ordered, low entropy sandcastle. 

Figure 5     The second law of thermodynamics

Entropy can be described by the following equation: 

ΔS = Q_rev/T
where ΔS = change in entropy,
Q_rev = heat introduced or lost in a reversible process,
T = temperature

We can see that as the heat in a system increases, the entropy increases.

Entropy can also be described by a second, equivalent equation:

ΔS = k × ln(W)
where ΔS = change in entropy,
k = Boltzmann's constant, approximately equal to 1.38 × 10⁻²³ J/K,
ln(W) = natural logarithm of W

In this context, W does not represent work, but rather the total number of possible microstates the system can adapt. A microstate refers to any combination of all possible orientations of particles within a system. Thus, since the number of microstates depends on the number of particles within a system, the entropy of a system tends to increase as more particles are added.

The Boltzmann constant, represented by k or k_B, is a fundamental constant used in several thermodynamic equations. While you may not need to memorize the exact quantity of this constant, it is useful to recognize that it is a defined constant.

d) Third law of thermodynamics

The third law of thermodynamics states that the entropy of a pure crystalline substance at absolute zero is equal to zero. If you take anything away from this law, just remember that lowering the temperature of a system will usually decrease the entropy as molecules are less able to move around.  

----

Part 4: Thermodynamic functions, systems, and processes 

a) Types of functions

Thermodynamic functions are generally described as either state or path functions.

State functions are properties that do not depend on the path taken to reach a value and depend only on the current state of the system. Examples of state functions are mass, pressure, temperature, volume, Gibbs free energy, enthalpy, entropy, among others.  

Path functions depend on the path taken to reach a certain value. Examples of path functions include heat and work.  

b) Types of systems

There are three types of systems that you may encounter on the MCAT: open, closed, or isolated. 

Open systems can exchange both matter and energy with the environment. Closed systems can exchange energy, but not matter, with the environment. Isolated systems can exchange neither energy nor matter with the environment.

Figure 6     Open, closed, and isolated systems

c) Types of processes

In our final section, we’ll cover four thermodynamic processes you should be familiar with: isothermal, adiabatic, isovolumetric, and isobaric. In each of these processes (except for one), a term from the first law of thermodynamics (remember: ∆U = Q – W) is held constant. 

Isothermal processes have a constant temperature, and as we discussed earlier, and therefore ∆U = 0. In adiabatic processes, heat is not exchanged and Q = 0. In isovolumetric processes, the volume cannot change, work cannot be done, and therefore W = 0. Finally, in isobaric processes, pressure is constant, but this does not affect our ∆U = Q – W equation. 

The most common way to depict these processes is with a P-V diagram in which pressure is plotted on the y-axis and volume is plotted on the x-axis. For any P-V diagram, the work done is the area under the curve for an open-loop process or the area inside the loop for a closed-loop process. 

Figure 7     A pressure-volume curve

Different values of heat capacity may be used in different contexts, based on whether the pressure or volume of the environment is allowed to change over time. In general, the specific heat capacity of a process occurring at constant pressure is usually higher than the specific heat capacity of a process occurring at constant volume. These two values are usually represented by c_p (constant-pressure heat capacity) and c_v (constant-volume heat capacity.

----

Part 5: High-yield terms and equations

Heat: the transfer of energy based on a temperature difference between two objects

Temperature: a measure of the average energy due to motion of particles in an object

Heat capacity: the heat required to raise the temperature of an object by a certain unit of temperature

Specific heat: the amount of heat required to raise one gram of an object by one degree Kelvin (or Celsius)

Phase changes: the transition between different phases of matter, such as from solid to liquid or from liquid to gas

Phase-change diagram: a diagram plotting temperature versus energy for a specific molecule that shows its phase changes

Heats of transformation: intrinsic property of a substance that defines the energy needed to generate a phase change

Heat of fusion: the heat of transformation constant for a solid to liquid transformation

Heat of vaporization: the heat of transformation constant for a liquid to gas transformation

Heat transfer: the transfer of heat from one object to another via conduction, convection, or radiation

Conduction: a direct transfer of heat through contact and without movement of the objects

Convection: a transfer of heat through the motion of a liquid or gas over another object

Radiation: an indirect transfer of heat through electromagnetic waves that does not require the two objects to be in contact

Coefficient of linear expansion: a constant intrinsic to a specific material that determines how susceptible it is to linear expansion when temperature is increased

Coefficient of volumetric expansion: a constant intrinsic to a specific material that determines how susceptible it is to volumetric expansion when temperature is increased

Zeroth law of thermodynamics: when two objects are in thermal equilibrium with a third object, the original two objects are in thermal equilibrium with each other

First law of thermodynamics: ∆U = Q – W

Second law of thermodynamics: the total entropy of an isolated system cannot decrease over time

Third law of thermodynamics: the entropy of a pure crystalline substance at absolute zero is equal to zero

State functions: properties that do not depend on the path taken to reach the value and depend only on the current state of the system

Path functions: depend on the path taken to reach a certain value

Open systems: exchange both matter and energy with the environment

Closed systems: exchange energy, but not matter, with the environment

Isolated systems: exchange neither energy nor matter with the environment

Isothermal processes: constant temperature and therefore ∆U = 0

Adiabatic processes: heat is not exchanged and Q = 0

Isovolumetric processes: the volume cannot change, work cannot be done, and therefore W = 0

Isobaric processes: pressure is constant

P-V diagram: a diagram in which pressure is plotted on the y-axis and volume is plotted on the x-axis, and the work done is the area under the curve for an open-loop process or the area inside the loop for a closed-loop process

Equations

Heat during phase change: q = m × L
Thermal expansion: ΔL = α × L × ΔT
Volumetric expansion: ΔV = β × V × ΔT
First law of thermodynamics: ΔU = Q − W
Entropy: ΔS = Q_rev/T

Not ready to commit to your MCAT prep at this time?

Enter your name and email for a free MCAT question delivered straight to your inbox daily.

----

Part 6: Thermodynamics practice passage  

Researchers are studying thermal equilibrium between cellular cytoplasm and various organelles in a panel of cancer stem cells. The researchers hypothesize that aberrations in this thermal equilibrium may produce malignant phenotypes by leading to upregulation of cellular stress proteins. 

Researchers devise an experiment in which the average temperatures of three organelles (mitochondria, Golgi apparatus, and rough endoplasmic reticulum) are measured and compared to the average cytoplasmic temperatures in cancer stem cells and healthy human cells. A microthermometer is used to obtain these values precisely and accurately, and for each individual reading, the temperature is measured every second for sixty seconds. Then, the individual readings for each organelle are averaged together to determine the final value. All differences were determined to be statistically significant.

The results from this experiment are shown in Table 1:

Table 1    Average temperature of different cellular locations

Average temperature	Healthy cells	Cancer stem cells
Cytoplasm	37.98 °C	37.98 °C
Mitochondria	37.97 °C	37.10 °C
Golgi apparatus	37.97 °C	38.12 °C
Rough endoplasmic reticulum	37.98 °C	37.82 °C

After obtaining the temperature measurements, the researchers want to test the effect of altered temperatures on the organelle volumes to see if this might partially explain the phenotypic differences between cancer stem cells and healthy cells. The coefficients of volumetric expansion for the mitochondria, Golgi apparatus, and rough endoplasmic reticulum are: 1.1 x 10^-3 K^-1, 1.4 x 10^-2 K^-1, and 1.9 x 10^-3 K^-1. The researchers hypothesize that the differences in size might lead to apoptosis.

In a final experiment, researchers measure the pressure and volume of the mitochondria over the course of two hours of ATP synthesis. The mitochondria are held at a constant temperature throughout the process. 

(Note: The information in this passage was created for the sole purpose of presenting an MCAT-style passage and should not be construed to be factually true.)

Question 1: Given the characterization of cytoplasm as a fluid, what type of heat transfer occurs between cytoplasm and organelles?

            A) Convection

            B) Radiation

            C) Conduction

            D) Isolation

Question 2: The researchers find that for a constant increase in temperature and the same starting volume, which of the following organelles has the biggest expansion in volume?

A) Mitochondria

            B) Rough endoplasmic reticulum

            C) Cytoplasm

            D) Golgi apparatus

Question 3: What type of system is normal heart cell in a living human?

A) Closed

            B) Open

            C) Isolated

            D) Adiabatic 

Question 4: What type of thermodynamic process is described in the final experiment?

A) Adiabatic

            B) Isothermal

            C) Isovolumetric

            D) Isobaric

Question 5: Researchers plot a closed-loop pressure versus volume curve of the results from the final experiment. The area inside the curve best represents which of the following?

A) Work

            B) Power

            C) Entropy

            D) Enthalpy 

Answer key for thermodynamics practice passage

1. Answer choice A is correct. Convection is a type of heat transfer that occurs when a liquid or gas moves over another object. In this case, the cytoplasm is a liquid that moves over the organelles, thereby directly transferring heat via convection (choice A is correct). Radiation is not direct and is mediated through electromagnetic waves. Since the cytoplasm and organelles are touching, radiation is not the type of heat transfer responsible in this case (choice B is incorrect). Conduction is a type of heat transfer that occurs when two solid objects come in contact, but the cytoplasm is a liquid (choice C is incorrect). Isolation is not one of the three types of heat transfer (choice D is incorrect). 

2. Answer choice D is correct. The equation for volumetric expansion is given by ∆V = β * V * ∆T where V is volume, β is the coefficient of volumetric expansion, and T is temperature. Here, we see that the coefficient of volumetric expansion and the change in volume are directly proportional. So, holding the temperature increase and starting volume constant, ∆V depends on β, and a bigger β will lead to a greater increase. The Golgi apparatus has the largest coefficient of volumetric expansion according to the passage (choice D is correct; choices A, B, and C are incorrect). 

3. Answer choice B is correct. All cells can exchange matter and energy with their surroundings, which makes them examples of an open system (choice B is correct; choices A, C, and D are incorrect).

4. Answer choice B is correct. The final experiment is described in the last paragraph of the passage, and the passage states that temperature is held constant. Temperature is held constant in isothermal processes (choice B is correct; choices A, C, and D are incorrect).

5. Answer choice A is correct. The area inside a closed-loop process on a pressure-volume curve is equal to the work done (choice A is correct; choices B, C, and D are incorrect). 

----

Part 7: Thermodynamics practice problems and answers 

Question 1: Which of the following best describes the second law of thermodynamics?

A)     Objects in motion tend to stay in motion

B)    Energy cannot be created or destroyed

C)     Entropy increases over time

D)    The entropy of a perfect crystal at absolute zero is equal to zero

Question 2: An actin filament can be modeled as a linear rod. Researchers determine the coefficient of linear expansion for actin to be 1.8 x 10^-1 K^-1. What is the increase in length of a 10 mm actin filament if the temperature of the cell is raised by 2 degrees Kelvin?

A)   1.05 mm

B)   21.9 mm

C)   3.60 mm

D)   36.0 mm

Question 3: Two solid objects at different initial temperatures are brought into contact with one another and achieve thermal equilibrium. The process that produces this form of heat transfer is:

A)    Conduction

B)    Convection

C)    Radiation

D)    Production

Question 4: Which of the following is not a state function?

A)     Heat

B)    Volume

C)    Gibbs free energy

D)    Enthalpy

Question 5: Researchers are studying Object A and Object B, and they determine that the average kinetic energy of the particles in Object A are greater than the average kinetic energy of the particles in Object B. Which of the following properties is greater in object A?

A)    Volume

B)    Temperature

C)    Enthalpy

D)    Gibbs free energy

Answer key for thermodynamics practice passage

1. Answer choice C is correct. The second law of thermodynamics discusses entropy and states that entropy increases over time unless there are restrictive forces (choice C is correct). Choice A is Newton’s first law. Choice B describes the law of conservation of energy. Choice D describes the third law of thermodynamics.

2. Answer choice C is correct. The formula for linear expansion is ∆L = α * L * ∆T, so all we need to do is plug in the numbers and solve for ∆L, which is the increase in length. Since you will not have a calculator on the exam, we can employ some simple tricks. First, look at the answer choices. Since all of the answer choices are in millimeters, you don’t need to worry about the scientific notation on this problem. So, we have simplified our calculation to ∆L = 0.18 * 10 * 2. All we need to do is to roughly determine the ballpark significant figures that will show up in our answer. 10 * 2 is 20, and we know that 20 * 0.18 is slightly less than 4 at 3.6 (choice C is correct; choices A, B, and D are incorrect). 

3. Answer choice A is correct. Conduction occurs when two solids are brought into contact with one another and transfer heat (choice A is correct). Convection occurs when a fluid flows over another object and produces a transfer of heat (choice B is incorrect). Radiation occurs when electromagnetic waves transfer heat between two objects that are not touching (choice C is incorrect). Production is not a commonly used form of heat transfer (choice D is incorrect).

4. Answer choice A is correct. Heat is a path function, not a state function (choice A is correct). Volume, Gibbs free energy, and enthalpy are state functions (choices B, C, and D are incorrect).

5. Answer choice B is correct. Temperature is a measure of the average kinetic energy of the particles in an object (choice B is correct). We do not have enough information to make a determination about volume, enthalpy, or Gibbs free energy (choices A, C, and D are incorrect).