Thermodynamics: Definition, Laws & Equations

For many people, thermodynamics sounds like some scary branch of physics that only the smart people can understand. But with some foundational knowledge and a little bit of work, anyone can make sense of this area of study.

Thermodynamics is a branch of physics that explores the goings-on in physical systems due to transfer of heat energy. Physicists from Sadi Carnot to Rudolf Clausius and James Clerk Maxwell to Max Planck have all had a hand in its development.

Definition of Thermodynamics

The word "thermodynamics" comes from the Greek roots thermos, meaning hot or warm, and dynamikos, meaning powerful, though later interpretations of the root attribute the meaning of action and motion to it. In essence, thermodynamics is the study of heat energy in motion.

Thermodynamics deals with how heat energy can be generated and transformed into different forms of energy such as mechanical energy. It also explores the notion of order and disorder in physical systems as well as energy efficiency of different processes.

A deep study of thermodynamics also relies heavily on statistical mechanics in order to understand kinetic theory and so on. The basic idea being that thermodynamic processes can be understood in terms of what all of the little molecules in a system are doing.

The problem is, however, that it is impossible to observe and account for each molecule’s individual action, so statistical methods are applied instead, and to great accuracy.

A Brief History of Thermodynamics

Some foundational work related to thermodynamics was developed as early as the 1600s. Boyle’s law, developed by Robert Boyle, determined the relationship between pressure and volume, which eventually led to the ideal gas law when combined with Charles’s law and Gay-Lussac’s Law.

It wasn’t until 1798 that heat was understood as a form of energy by Count Rumford (aka Sir Benjamin Thompson). He observed that heat generated was proportional to work done in turning a boring tool.

In the early 1800s, French military engineer Sadi Carnot did a considerable amount of work in developing the concept of a heat engine cycle, as well as the idea of reversibility in a thermodynamic process. (Some processes work just as well backwards in time as forwards in time; those processes are called reversible. Many other processes only work in one direction.)

Carnot’s work led to the development of the steam engine.

Later, Rudolf Clausius formulated the first and second laws of thermodynamics, which are described later in this article. The field of thermodynamics evolved rapidly in the 1800s as engineers worked to make steam engines more efficient.

Thermodynamic Properties

Thermodynamic properties and quantities include the following:

  • Heat, which is energy transferred between objects at different temperatures.
  • Temperature, which is a measure of the average kinetic energy per molecule in a substance.
  • Internal energy, which is the sum of the molecular kinetic energy and potential energy in a system of molecules. 
  • Pressure, which is a measure of the force per unit area on a container which houses a substance.
  • Volume is the three-dimensional space that a substance takes up.
  • Microstates are the states that individual molecules are in.
  • Macrostates are the larger states that collections of molecules are in.
  • Entropy is a measure of the disorder in a substance. It is mathematically defined in terms of microstates, or equivalently, in terms of changes in heat and temperature.

Definition of Thermodynamic Terms

Many different scientific terms are used in the study of thermodynamics. In order to simplify your own investigations, here is a list of definitions of commonly used terms:

  • Thermal equilibrium or thermodynamic equilibrium: A state in which all parts of a closed system are at the same temperature.
  • Absolute zero Kelvin: Kelvin is the SI unit for temperature. The lowest value on this scale is zero, or absolute zero. It is the coldest possible temperature.
  • Thermodynamic system: Any closed system that contains interactions and exchanges of thermal energy.
  • Isolated system: A system that cannot exchange energy with anything outside of it.
  • Heat energy or thermal energy: There are many different forms of energy; among them is thermal energy, which is the energy associated with the kinetic motion of the molecules in a system. 
  • Gibbs free energy: A thermodynamic potential that is used to determine the maximum amount of reversible work in a system.
  • Specific heat capacity: The amount of heat energy required to change the temperature of a unit mass of a substance by 1 degree. It depends on the type of substance and is a number usually looked up in tables.
  • Ideal gas: A simplified model of gases that applies to most gases at standard temperature and pressure. The gas molecules themselves are assumed to collide in perfectly elastic collisions. It is also assumed that the molecules are very far enough apart from each other that they can be treated like point masses. 

The Laws of Thermodynamics

There are three main laws of thermodynamics (called the first law, second law and third law) but there is also a zeroth law. These laws are described as follows:

The zeroth law of thermodynamics is probably the most intuitive. It states that if substance A is in thermal equilibrium with substance B, and substance B is in thermal equilibrium with substance C, then it follows that substance A must be in thermal equilibrium with substance C.

The first law of thermodynamics is basically a statement of the law of conservation of energy. It states that the change in internal energy of a system is equal to the difference between the heat energy transferred into the system and the work done by the system on its surroundings.

The second law of thermodynamics, sometimes referred to as the law that implies an arrow of time – states that the total entropy in a closed system can only remain constant or increase as time moves forward. Entropy can be thought of loosely as a measure of the disorder of a system, and this law can be thought of loosely as stating that “things tend to mix together the more you shake them up, as opposed to unmixing.”

The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature of a system approaches absolute zero. Since at absolute zero, there is no molecular motion, it makes sense that the entropy would not change at that point.

Statistical Mechanics

Thermodynamics makes use of statistical mechanics. This is a branch of physics that applies statistics to both classical and quantum physics.

Statistical mechanics allows scientists to work with macroscopic quantities in a more straightforward manner than with microscopic quantities. Consider temperature, for example. It is defined as the average kinetic energy per molecule in a substance.

What if instead you needed to determine the actual kinetic energy of each molecule, and more than that, keep track of each collision between molecules? It would be nearly impossible to make any headway. Instead, statistical techniques are used that allow for an understanding of temperature, heat capacity and so on as larger properties of a material.

These properties describe average behavior going on within the material. The same is true of quantities like pressure and entropy.

Heat Engines and Steam Engines

A heat engine is a thermodynamic system that converts heat energy into mechanical energy. Steam engines are an example of a heat engine. They work by using high pressure to move a piston.

Heat engines operate on some sort of complete cycle. They have some sort of heat source, which is usually called the heat bath, that allows them to take in heat energy. That heat energy then causes some sort of thermodynamic change within the system, such as increasing pressure or expanding a gas.

When a gas expands, it does work on the environment. Sometimes this looks like causing a piston to move in an engine. At the end of a cycle, a cool bath is used to bring the system back to its starting point.

Efficiency and the Carnot Cycle

Heat engines take in heat energy, use it to do useful work and then also give off or lose some heat energy to the environment during the process. The efficiency of a heat engine is defined as the ratio of the useful work output to the net heat input.

Not surprisingly, scientists and engineers want their heat engines to be as efficient as possible – converting maximum amounts of heat energy input into useful work. You might think that the most efficient an heat engine could be is 100 percent efficient, but this is incorrect.

In fact, there is a limit on the maximum efficiency of a heat engine. Not only does the efficiency depend on the type of processes in the cycle, even when the best possible processes (ones that are reversible) are used, the most efficient a heat engine can be depends on the relative difference in temperatures between the heat bath and the cool bath.

This maximum efficiency is called the Carnot efficiency, and it is the efficiency of a Carnot cycle, which is a heat engine cycle made up of entirely reversible processes.

Other Applications of Thermodynamics

There are many applications of thermodynamics to processes seen in everyday life. Take your refrigerator, for example. A refrigerator operates off of a thermodynamic cycle.

First a compressor compresses refrigerant vapor, which causes a rise in pressure and pushes it forward into coils located on the outside back of your refrigerator. If you feel these coils, they will feel warm to the touch.

The surrounding air causes them to cool, and the hot gas turns back into a liquid. This liquid cools down at high pressure as it flows into coils inside the fridge, absorbing heat and cooling down the air. Once hot enough, it evaporates into gas again and goes back into the compressor, and the cycle repeats.

Heat pumps, which can heat and cool your house, work on similar principles.