MCAT Physics and Math Review

Chapter 3: Thermodynamics

3.4 Second Law of Thermodynamics and Entropy

The second law of thermodynamics states that objects in thermal contact and not in thermal equilibrium will exchange heat energy such that the object with a higher temperature will give off heat energy to the object with a lower temperature until both objects have the same temperature at thermal equilibrium. As such, energy is constantly being dispersed.


Consider each of the following scenarios: hot tea cooling down, a frozen drink melting, iron rusting, buildings crumbling, balloons deflating, and living things dying and decaying. These scenarios share a common denominator. In each of them, energy of some form is going from being localized or concentrated to being spread out or dispersed. The thermal energy in the hot tea is spreading out to the cooler air that surrounds it. The thermal energy in the warmer air is spreading out to the cooler frozen drink. The chemical energy in the bonds of elemental iron and oxygen is released and dispersed as a result of the formation of the more stable, lower-energy bonds of iron oxide (rust). The potential energy of the building is released and dispersed in the form of light, sound, and heat as the building crumbles and falls. The energy of the pressurized air is released to the surrounding atmosphere as the balloon deflates. The chemical energy of all the molecules and atoms in living flesh is released into the environment during the process of death and decay.


The second law of thermodynamics states that energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so. Pay attention to this: the usual way of thinking about entropy as “disorder” must not be taken too literally, a trap that many students fall intoBe very careful in thinking about entropy as disorder. The old analogy between a messy (disordered) room and entropy is deficient and may not only hinder understanding but actually increase confusion.

Entropy is the measure of the spontaneous dispersal of energy at a specific temperature: how much energy is spread out, or how widely spread out energy becomes in a process. In the discussion of microstates earlier, we considered that when ice melts, the freedom of movement of the water molecules increases. If the water remains at the melting point, it will have the same average kinetic energy as molecules of ice; the difference between the two is the number of available microstates. That is, while both water and ice at 0°C have the same kinetic energy, the energy is dispersed over a larger number of microstates in liquid water. Liquid water therefore has higher entropy and, by extension, it is indeed less organized than ice. The equation for calculating the change in entropy is:

Equation 3.7

where ΔS is the change in entropy, Qrev is the heat that is gained or lost in a reversible process, and is the temperature in kelvin. The units of entropy are usually  . When energy is distributed into a system at a given temperature, its entropy increases. When energy is distributed out of a system at a given temperature, its entropy decreases.


If, in a reversible process, 6.66 × 104 J of heat is used to change a 200 g block of ice to water at a temperature of 273 K, what is the change in the entropy of the system? (Note: The heat of fusion of ice  )


We know that during a phase change, the temperature is constant; in this case, 273 K. From the information given,

The amount of heat was exactly enough to completely melt the block of ice without changing the temperature of the resulting liquid water; therefore, T is constant.

Notice that the second law states that energy will spontaneously disperse; it does not say that energy can never be localized or concentrated. However, the concentration of energy will rarely happen spontaneously in a closed system. Work usually must be done to concentrate energy. For example, refrigerators work against the direction of spontaneous heat flow (that is, they counteract the flow of heat from the “warm” exterior of the refrigerator to the “cool” interior), thereby “concentrating” energy outside of the system in the surroundings. As a result, refrigerators consume a lot of energy to accomplish this movement of energy against the temperature gradient.

The second law has been described as time’s arrow because there is a unidirectional limitation on the movement of energy by which we recognize before and after or new and old. For example, you would instantly recognize whether a video recording of an explosion was running forward or backward. Another way of understanding this is to say that energy in a closed system will spontaneously spread out and entropy will increase if it is not hindered from doing so. Remember that a system can be variably defined to include the entire universe; in fact, the second law ultimately claims that the entropy of the universe is increasing.

ΔSuniverse = ΔSsystem + ΔSsurroundings > 0

Equation 3.8

When describing processes, physicists often use terms such as natural, unnatural, reversible, or irreversible. These terms confuse students but needlessly so because these terms are descriptive of observable phenomena. For example, we expect that when a hot object is brought into thermal contact with a cold object, the hot object will transfer heat energy to the cold object until both are in thermal equilibrium (that is, at the same temperature). This is a natural process and also one that we would describe as irreversible: we are not surprised that the two objects eventually reach a common temperature, but we would be shocked if all of a sudden the hot object became hotter and the cold object became colder. This would be an unnatural process.


The universe is a closed, expanding system, so you know that the entropy of the universe is always increasing. The more space that appears with the expansion of the universe, the more space there is for the entire universe’s energy to be distributed and the total entropy of the universe to increase irreversibly.

To define a reversible reaction, let’s consider a system of ice and liquid water in equilibrium at 0°C. If we place this mixture of ice and liquid water into a thermostat (device for regulating temperature) that is also at 0°C and allow infinitesimal amounts of heat to be absorbed by the ice from the thermostat so that the ice melts to liquid water at 0°C and the thermostat remains at 0°C, then the increase in the entropy of the system (the water) will be exactly equal to the entropy decrease of the surroundings (the thermostat). The net change in the entropy of the system and its surroundings is zero. Under these conditions, the process is reversible. The key to a reversible reaction is making sure that the process goes so slowly—requiring an infinite amount of time—that the system is always in equilibrium and no energy is lost or dissipated. To be frank, no real processes are reversible; we can only approximate a reversible process. Note how physicists define reversible processes: These are processes that can spontaneously reverse course. For example, while water can be put through cycles of freezing and melting innumerable times, ice melting on the warm countertop would not be expected to suddenly freeze if it remains in the warm environment. The liquid water will need to be placed in an environment that is cold enough to cause the water to freeze, and once frozen in the cold environment, the ice would not be expected to begin melting spontaneously. The freezing and melting of water in real life are therefore irreversible processes in physics while still being chemically reversible.

MCAT Concept Check 3.4:

Before you move on, assess your understanding of the material with these questions.

1.    Describe entropy on a macroscopic level and in statistical terms.

·        Macroscopic:

·        Statistical:

2.    What is the relationship between the entropy of a system and its surroundings for any thermodynamic process?