Definition of Thermal Equilibrium

1. Thermal equilibrium is a physical phenomenon in which a uniform distribution of heat is produced between two or more bodies of a system after an energy transfer process, from the largest to the smallest, until all are in the same condition. That is, they have the same temperature. Example: On a tray, there is a hot sandwich and a cold drink. After a few minutes of transfer with the environment, the snack will lose heat, and the drink will receive heat, in such a way that both will end up with the same temperature.

Grammatical category: masculine noun
in syllables: e-qui-li-brio + tér-mi-co.

Thermal equilibrium

Evelyn Maitee Marin
Industrial Engineer, MSc in Physics, and EdD

Thermal equilibrium refers to a state in which two bodies that were initially at different temperatures manage to equalize it through a heat transfer process, which can occur by different methods: conduction (the bodies are required to be in physical contact ), by convection (when a fluid is found between the bodies) or radiation (it is carried out through electromagnetic waves). From a microscopic perspective, thermal equilibrium is reached when the thermal energy between the bodies is equal, since the temperature is related to the thermal energy of the particles that make up the bodies.

The direction in which heat transfer occurs before reaching a state of thermal equilibrium, that is, the temperature gradient, is always from the body that is at a higher temperature to the body that has a lower temperature. Once thermal equilibrium is reached, the temperature of the two bodies will be the same.

If we hold a cup with our hands that contains a hot liquid inside, we can feel how the skin of the hands that is in contact with the cup heats up. After a certain time, the liquid contained in the cup, the cup and the skin of the palm of the hands reach thermal equilibrium, that is, part of the heat of the liquid was transferred to the cup and the hands until the temperatures were equal ( assuming no heat transfer with the surrounding air).

On what does it depend that the bodies reach a thermal equilibrium?

As mentioned, the state of thermal equilibrium is the result of a heat transfer process, and this does not occur instantaneously, since it depends on the material of each body (the specific heat of the material), the mass of the themselves and the temperature difference between them. It can then be said that for heat transfer to occur between two bodies, they must interact (by contact or at a distance) being at different temperatures, and for them to reach thermal equilibrium, the temperatures of both must be equal.

Difference Between Heat and Temperature

Until now, the definition of thermal equilibrium has cited two terms that in everyday use are often used interchangeably and sometimes erroneously. Each one is described below:

Temperature (T): is a scalar physical quantity that is linked to the thermal energy that a system or body possesses and can be expressed in absolute scales (such as Kelvin or Rankine), or in relative scales (such as Celsius or Fahrenheit). Temperature is classified as a statistical magnitude, which means that to measure it, thermometric magnitudes are used, for this reason, thermometers use dimensions that vary with temperature, such as the pressure of a gas, the height of a column of mercury , infrared radiation or an electrical resistance.

The scale shown by the thermometer is calibrated to establish an equivalent between the height of the mercury column inside the cylinder and the temperature value. In the image, the thermometer registers a temperature of 36.4 °C.

Heat (Q): It is a flow of energy that occurs between two or more bodies through the border of said system due to the difference in temperature. Heat can be expressed in calories (cal), which refers to the amount of energy required to increase the temperature of 1 g of water from 14.5°C to 15.5°C. In the English system, the Btu (British Thermal Unit) is used to denote thermal energy.

Note: Although heat refers to the amount of energy that is exchanged during a heat transfer process, in Physics, different units are often used to refer to energy associated with mechanical processes (Joule) and energy associated with thermal processes. (Btu or cal), although there is an equivalence between these units, for example, 1 cal = 4.1869 J.

The following expression is used to determine the heat (Q) that is transferred between a body of mass “m” and its surroundings as soon as there are differences in temperature ΔT between them:

Where “c” is the specific heat of the body or substance, or also called, heat capacity per unit mass.

To better understand the difference between the concepts of temperature and heat, suppose that two containers are placed in a freezer overnight: one made of aluminum and the other made of cardboard, after all those hours, the space in the freezer, the aluminum container and the cardboard one enters thermal equilibrium, which means that they are all at the same temperature; however, if we touch the aluminum container with our fingers, we feel that it feels “colder” than the cardboard container. This is because despite the fact that the two are at the same temperature, the heat transfer capacity of aluminum is greater than that of cardboard (in general, metals tend to be good thermal conductors and non-metals are not).

Banks, trees and snow are in thermal equilibrium, that is, they are all at the same temperature, although the heat transfer capacity of the materials (wood, leaves, water) is different.

The zeroth law of thermodynamics

This law is also known as the law of equilibrium, since it refers to the state of thermal equilibrium between three bodies A, B and C and was proposed by the British physicist and astronomer Ralph H. Fowler in 1931 and states that:

“If two bodies A and B are separately in thermal equilibrium with another body C, then it follows that bodies A and B are in thermal equilibrium with each other.”

The image shows the famous photograph taken during the conference “Photons and electrons” (the Solvay Conference) in the year 1927 where some of the most outstanding scientists in history were. Ralph H. Fowler stands out in the green circle.

Bodies can be objects or systems; for example, body C can be a thermometer. If we introduce the thermometer (body C) into a container with a liquid (body A) until the thermometer is in thermal equilibrium with the liquid A, that is, when the temperature indicated by the thermometer remains constant, and apart we introduce the same thermometer C inside another container that contains a different fluid (body B) and we note that when the thermometer reaches thermal equilibrium with body B it marks the same temperature that it marked in A, we can say that the three bodies A, B and C meet in thermal equilibrium.

If A and C are in thermal equilibrium and B and C are also in thermal equilibrium, then A and B are in thermal equilibrium, and therefore the temperatures of A, B, and C are equal.



Serway Raymond (2015). Physics for science and engineering. Volume 1. Ninth edition. Cengage Learning. p. 594