Third Law Of Thermodynamics: Definition, Equation & Examples

The laws of thermodynamics help scientists understand thermodynamic systems. The third law defines absolute zero and helps to explain that the entropy, or disorder, of the universe is heading towards a constant, nonzero value.

Entropy is often described in words as a measure of the amount of disorder in a system. This definition was first proposed by Ludwig Boltzmann in 1877. He defined entropy mathematically like this:

\(S=k\ln{Y}\)

In this equation, ​Y​ is the number of microstates in the system (or the number of ways the system can be ordered), ​k​ is the Boltzmann constant (which is found by dividing the ideal gas constant by Avogadro's constant: 1.380649 × 10⁻²³ J/K) and ​ln​ is the natural logarithm (a logarithm to the base ​e​).

Two big ideas demonstrated with this formula are:

1. Entropy can be thought of in terms of heat, specifically as the amount of thermal energy in a closed system, which is not available to do useful work.
2. The more microstates, or ways of ordering a system, the more entropy the system has.

Additionally, the change in entropy of a system as it moves from one macrostate to another can be described as:

\(\Delta S = \int \dfrac {dQ}{T}\)

where ​T​ is temperature and ​Q​ is the heat exchanged in a reversible process as the system moves between two states.

The second law of thermodynamics states that the total entropy of the universe or an isolated system never decreases. In thermodynamics, an isolated system is one in which neither heat nor matter can enter or exit the system's boundaries.

In other words, in any isolated system (including the universe), entropy change is always zero or positive. What this essentially means is that random processes tend to lead to more disorder than order.

An important emphasis falls on the ​tend to​ part of that description. Random processes ​could​ lead to more order than disorder without violating natural laws, but it is just vastly less likely to happen.

Eventually, the change in entropy for the universe overall will equal zero. At that point, the universe will have reached thermal equilibrium, with all energy in the form of thermal energy at the same nonzero temperature. This is often referred to as the heat death of the universe.

Most people around the world discuss temperature in degrees Celsius, while a few countries use the Fahrenheit scale. Scientists everywhere, however, use Kelvins as their fundamental unit of absolute temperature measurement.

This scale is built on a particular physical basis: Absolute zero Kelvin is the temperature at which all molecular motion ceases. Since heat ​is​ molecular motion in the simplest sense, no motion means no heat. No heat means a temperature of zero Kelvin.

Note that this is different from a freezing point, like zero degrees Celsius – molecules of ice still have small internal motions associated with them, also known as heat. Phase changes between solid, liquid and gas, however, do lead to massive changes in entropy as the possibilities for different molecular organizations, or microstates, of a substance suddenly and rapidly either increase or decrease with the temperature.

The third law of thermodynamics states that as the temperature approaches absolute zero in a system, the absolute entropy of the system approaches a constant value. This was true in the last example, where the system was the entire universe. It is also true for smaller closed systems – continuing to chill a block of ice to colder and colder temperatures will slow down its internal molecular motions more and more until they reach the least disordered state that is physically possible, which can be described using a constant value of entropy.

Most entropy calculations deal with entropy differences between systems or states of systems. The difference in this third law of thermodynamics is that it leads to well-defined values of entropy itself as values on the Kelvin scale.

To become perfectly still, molecules must also be in their most stable, ordered crystalline arrangement, which is why absolute zero is also associated with perfect crystals. Such a lattice of atoms with only one microstate is not possible in reality, but these ideal conceptions underpin the third law of thermodynamics and its consequences.

A crystal that is not perfectly arranged would have some inherent disorder (entropy) in its structure. Because entropy can also be described as thermal energy, this means it would have some energy in the form of heat – so, decidedly ​not​ absolute zero.

Although perfect crystals do not exist in nature, an analysis of how entropy changes as a molecular organization approaches one reveals several conclusions:

•The more complex a substance – say C₁₂H₂₂O₁₁ vs. H₂ – the more entropy it is bound to have, as the number of possible microstates increases with the complexity.
•Substances with similar molecular structures have similar entropies.
•Structures with smaller, less energetic atoms and more directional bonds, like hydrogen bonds, have ​less​ entropy as they have more rigid and ordered structures.

While scientists have never been able to achieve absolute zero in laboratory settings, they get closer and closer all the time. This makes sense because the third law suggests a limit to the entropy value for different systems, which they approach as the temperature drops.

Most importantly, the third law describes an important truth of nature: Any substance at a temperature greater than absolute zero (thus, any known substance) must have a positive amount of entropy. Furthermore, because it defines absolute zero as a reference point, we are able to quantify the relative amount of energy of any substance at any temperature.

This is a key difference from other thermodynamic measurements, such as energy or enthalpy, for which there is no absolute reference point. Those values make sense only relative to other values.

Putting together the second and third laws of thermodynamics leads to the conclusion that eventually, as all energy in the universe changes into heat, it will reach a constant temperature. Called thermal equilibrium, this state of the universe is unchanging, but at a temperature ​higher​ than absolute zero.

The third law also supports implications of the first law of thermodynamics. This law states that the change in internal energy for a system is equal to the difference between the heat added to the system and the work done by the system:

\(\Delta U = Q-W\)

Where ​U​ is energy​, Q​ is heat and ​W​ is work, all typically measured in joules, Btus or calories).

This formula shows that more heat in a system means it will have more energy. That in turn necessarily means more entropy. Think of a perfect crystal at absolute zero – adding heat introduces some molecular motion, and the structure is no longer perfectly ordered; it has some entropy.