# Examples of Thermal Equilibrium

When two bodies that are at different temperatures are put in contact, the one that is hotter gives up part of its energy to the one with less temperature, to the point where both temperatures are equal.

This situation is known as thermal equilibrium, and it is precisely the state in which the temperatures of two bodies that initially had different temperatures are equal. It happens that when the temperatures equalize, the heat flow is suspended, and then the equilibrium situation is reached.

Theoretically, thermal equilibrium is fundamental in what is known as the Zero Law or the Zero principle of thermodynamics, which explains that if two separate systems are at the same time in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This Law is fundamental to the entire discipline of thermodynamics, which is the branch of physics that deals with describing equilibrium states at a macroscopic level.

### Equilibrium heat quantity

The equation which gives rise to the quantification of the amount of heat that is exchanged in the transfers between the bodies, has the form:

Q = M * C * ΔT

Q being the amount of heat expressed in calories, M the mass of the body under study, C the specific heat of the body, and ΔT the temperature difference.

In an equilibrium situation, the mass and the specific heat retain their original value, but the temperature difference becomes 0 because it was precisely defined in the equilibrium situation where there are no temperature changes.

### Equilibrium temperature

Another important equation for the idea of ​​thermal equilibrium is the one that seeks to express the temperature that the unified system. It is accepted that when a system of N1 particles, which is at temperature T1, is put in contact with another system of N2 particles that is at temperature T2, the equilibrium temperature is obtained by the formula:

(N1 * T1 + N2 * T2) / (N1 + N2)

In this way, it can be seen that when both subsystems have the same number of particles, the equilibrium temperature is reduced to an average between the two initial temperatures. This can be generalized for relationships between more than two subsystems.

### Examples of thermal equilibrium

Here are some examples of situations where thermal equilibrium occurs:

1. Measuring body temperature through a thermometer works that way. The long duration that the thermometer must have in contact with the body to be able to truly quantify the degrees of temperature is due precisely to the time it takes to reach thermal equilibrium.
2. Products that are sold ‘natural’ could have passed through a refrigerator. However, after some time outside the refrigerator, in contact with the natural environment, they reached thermal equilibrium with it.
3. The permanence of glaciers in the seas and at the poles is a particular case of thermal equilibrium. Precisely, the warnings regarding global warming have a lot to do with an increase in the temperature of the seas, and then a thermal equilibrium where much of that ice melts.
4. When a person comes out of bathing, they are relatively cold because the body had come into equilibrium with the hot water, and now it must come into equilibrium with the environment.
5. When looking to cool a cup of coffee, adding cold milk to it.
6. Substances such as butter are very sensitive to changes in temperature, and with a very short time in contact with the environment at natural temperature, they come into equilibrium and melt.
7. By putting your hand on a cold railing, for a time, the hand becomes colder.
8. A jar with a kilo of ice cream will melt slower than another with a quarter of a kilo of the same ice cream. This is produced by the equation in which the mass determines the characteristics of the thermal equilibrium.
9. When an ice cube is placed in a glass of water, a thermal equilibrium also occurs. The only difference is that equilibrium implies a change of state, because it goes through 100 ° C where the water goes from a solid to a liquid.
10. Add cold water to a rate of hot water, where equilibrium is reached very quickly at a temperature colder than the original.