# Definition:Temperature

## Definition

**Temperature** is a physical property of matter that quantifies how hot or cold a body is.

It is a scalar quantity which can be mapped directly to the real number line.

### Absolute Temperature

**Absolute temperature** is a measure of the amount of heat energy in a body.

It is defined as:

- $T = \dfrac 1 k \paren {\dfrac {\partial U} {\partial \ln g} }$

where:

- $k$ is a constant that relates the mean kinetic energy and
**absolute temperature**of the body $B$ - $U$ is the total energy of $B$
- $g$ is the number of possible states in which $B$ can be.

### Dimension

**Temperature** is frequently, at elementary levels at least, considered as one of the fundamental dimensions of physics.

In dimensional analysis it is usually assigned the symbol $\Theta$.

## Scales

There are several scales against which **temperature** is measured.

Each one has two reference points.

Name | Unit symbol | Absolute Zero | Melting point of water | Boiling point of water |
---|---|---|---|---|

Celsius | ${}^\circ \mathrm C$ | $-273.15 \ {}^\circ \mathrm C$ | $0 \ {}^\circ \mathrm C$ | $99.9839 \ {}^\circ \mathrm C$ |

Fahrenheit | ${}^\circ \mathrm F$ | $-459.67 \ {}^\circ \mathrm F$ | $32 \ {}^\circ \mathrm F$ | $211.9710 \ {}^\circ \mathrm F$ |

Kelvin | $\mathrm K$ | $0 \ \mathrm K$ | $273.15 \ \mathrm K$ | $373.1339 \ \mathrm K$ |

Rankine | ${}^\circ \mathrm R$ | $0 \ {}^\circ \mathrm R$ | $491.67 \ {}^\circ \mathrm R$ | $671.641 \ {}^\circ \mathrm R$ |

There are others.

As a general rule, only Kelvin is used in physics nowadays.

Celsius is usually used in the domestic context, for weather reporting and so on, in most nations, and sometimes seen in the teaching of physics, but usually at the most elementary levels in schools.

Fahrenheit is still used as the official temperature scale only in the US and Belize, although can still be seen on occasion in the contexts of weather reporting and health monitoring in the UK.

The Rankine scale is used in a few specialist engineering applications in the US and Canada.

## Sources

- 1921: C.E. Weatherburn:
*Elementary Vector Analysis*... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $1$. Scalar and vector quantities - 1951: B. Hague:
*An Introduction to Vector Analysis*(5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $1$. Scalar and Vector Quantities - 1960: M.B. Glauert:
*Principles of Dynamics*... (previous) ... (next): Chapter $1$: Vector Algebra: $1.1$ Definition of a Vector - 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 22$: Vectors and Scalars - 1970: George Arfken:
*Mathematical Methods for Physicists*(2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach - 1992: Frederick W. Byron, Jr. and Robert W. Fuller:
*Mathematics of Classical and Quantum Physics*... (previous) ... (next): Volume One: Chapter $1$ Vectors in Classical Physics: $1.1$ Geometric and Algebraic Definitions of a Vector