# Temperature

Definition of temperature: The temperature is the thermodynamic magnitude that shows the thermal energy of one body in relation to another.

Although the definition of temperature is simple and concise, you can explain what the temperature is in a more extensive way:

### What is the temperature?

Temperature is a physical quantity of matter that quantifies the common notions of heat and cold. The objects of low temperature perceive them cold, while objects of higher temperatures we consider them warm or hot. This physiological sensation of cold and heat is generated when there is an exchange of thermal energy between the human body and other bodies or, simply, the environment that surrounds it.

From the physical point of view, the temperature of a substance can be defined, according to the molecular theory, as the measure of the average kinetic energy of the molecules that form it. On the other hand, the temperature can be defined according to statistical mechanics, as the derivative of energy with respect to entropy at constant volume.

In this sense, temperature is a magnitude that describes a macroscopic state and has an exclusively statistical character; therefore, it makes no sense to speak of the temperature of an isolated material particle, but of a set in which the law of large numbers is applicable.

Thermometers are the tool to measure the temperature quantitatively, which can be calibrated with respect to different temperature scales (Celsius scale, Kelvin scale or Fahrenheit scale).

## Scales to measure temperature

Since entropy, as a quantity that expresses the degree of disorder of a thermodynamic system, has no dimensions, the definition of statistical mechanics shows that temperature can be measured in the same units as energy. Traditionally, however, temperature scales have been created in parallel with the energy units. The factor that allows to pass from a system of units of energy to a temperature is called the Boltzmann constant.

The three most common scales to measure temperature are:

• The Celsius scale. Measure in degrees centigrade.
• The Kelvin scale. Measurement in Kelvin degrees (currently Kelvin)
• The Fahrenheit scale. Measure in degrees Fahrenheit.

Almost everyone uses the Celsius scale (° C) for the measurement of most temperatures. The temperature variation between one degree and the next in a Celsius scale is the same variation as in a Kelvin scale. The difference between the Celsius and Kelvin scales is in the fixation of its null point: in the Celsius scale the 0ºC correspond to the freezing point of water. This temperature expressed in the kelvin scale corresponds to 273.15 kelvins (273.15 K). The zero point of the Kelvin scale, the 0 kelvin, corresponds to the minimum temperature at which a body could theoretically reach. Colder than the 0 kelvin is impossible.

The intervals of the Kelvin scale are measured in Kelvin, but previously they were called Kelvin degrees.

However, there are a few countries, especially the United States, where the Fahrenheit scale is still used in daily life. It is a historical temperature scale in which the freezing point of water is at 32 ° F and the boiling temperature of water is at 212 ° F.

### Measurement of temperature in the international measurement system

The unit of measurement of the temperature in the International System of Units (SI) is the Kelvin. The Kelvin is, therefore, the unit used by scientists. It is common to see it referenced as Kelvin degree.

For practical purposes of measuring temperature within the fields of science, the International System of Units (SI) defines a scale and a unit for thermodynamic temperature based on the triple point of water. The triple point is that in which the solid state, the liquid state and the gaseous state of a substance coexist in equilibrium. It is defined with a temperature and a vapor pressure. The triple point of water is a second easily reproducible reference point.

For historical reasons, the triple point of water has been set at 273.16 units of the measuring range. This interval is called kelvin (in lowercase) represented by the symbol K (capitalized) in honor of the Scottish physicist William Thomson (Lord Kelvin) who defined the scale for the first time. It was previously called Kelvin grade.

## Temperature and thermodynamics

One of the main properties studied in the field of thermodynamics is temperature. In thermodynamics, temperature differences between different regions of matter are especially important. These differences are those that allow the movement of heat from one region to another. The heat is that it is the transfer of thermal energy.

Spontaneously, the heat flows only from the regions of higher temperature in the regions of lower temperature. As it is established in the second law of thermodynamics in the Clausius statement. So if heat is not transferred between two objects it is because both objects have the same temperature.

According to the approach of classical thermodynamics, the temperature of an object varies proportionally to the velocity of the particles it contains. It does not depend on the number of particles (of the mass) but on its average speed: the higher the temperature, the higher the average speed. Therefore, the temperature is directly linked to the average kinetic energy of the particles that move in relation to the center of mass of the object.

The temperature is an intensive variable, since it is independent of the quantity of the particles contained in the interior of an object, be they atoms, molecules or electrons. It is a property that does not depend on the amount of substance or the type of material.

## Temperature and thermal energy

The molecules of all material substances (solids, liquids and gases) are always in a continuous state of vibration or agitation, due to the multiple interactions that they suffer within the body. Consequently to this random agitation, the atoms and molecules of the matter possess certain internal energy, since they have kinetic energy in the form of movement and also potential energy due to the forces exerted between the particles.

Internal energy is also known as the thermal energy of bodies.

On the other hand, temperature is the magnitude that allows recording the average value of the thermal energy of a body.

## Temperature measurement

In order to determine the temperature of a system, it must be in thermodynamic equilibrium. It can be considered that the temperature varies with the position only if for each point there is a small area around it that can be treated as a thermodynamic system in equilibrium. In statistical thermodynamics, degrees of freedom are spoken of instead of particles.

Within the field of thermodynamics, it is said that a system is in a state of thermodynamic equilibrium, if it is unable to spontaneously experience any change of state or thermodynamic process when it is subjected to certain boundary conditions.

### Thermal equilibrium

In a more fundamental approach, the empirical definition of temperature is derived from the conditions of thermal equilibrium, which are expressed at the zero principle of thermodynamics.

When two systems are in thermal equilibrium they have the same temperature. The extension of this principle as an equivalence relation between several systems basically justifies the use of the thermometer and establishes the principles of its construction for its measurement. Although the zero law of thermodynamics would allow the empirical definition of many temperature scales, the second law of thermodynamics selects a single definition as the preferred one: absolute temperature, known as thermodynamic temperature.

This function corresponds to the variation of the internal energy with respect to changes in the entropy of a system. Its natural, intrinsic or zero point is the absolute zero, where the entropy of any system is minimal. Although this is the absolute minimum temperature described by the model, the third law of thermodynamics postulates that absolute zero can not be reached by any physical system.

### How is the temperature measured?

Currently, there are several ways to measure the temperature. Normally the different systems depend on the application or on whether very high or very low temperatures have to be measured. However, the most well-known and used tool is the thermometer.

Variations in the thermal state of a body cause changes in some macroscopic properties (dilation, evolution of electrical resistance, creation of electromotive forces, changes in pressure or volume in a gas, etc.). Consequently, the variations of these properties allow to be used for the construction of instruments that detect temperature variations.

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Last review: November 9, 2016

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