# 3.10: Temperature: Random Motion of Molecules and Atoms

Learning Objectives

• To identify the different between temperature and heat
• To recognize the different scales used to measuring temperature

The concept of temperature may seem familiar to you, but many people confuse temperature with heat. Temperature is a measure of how hot or cold an object is relative to another object (its thermal energy content), whereas heat is the flow of thermal energy between objects with different temperatures. Temperature is a measure of the average kinetic energy of the particles in matter. In everyday usage, temperature indicates a measure of how hot or cold an object is. Temperature is an important parameter in chemistry. When a substance changes from solid to liquid, it is because there was in increase in the temperature of the material. Chemical reactions usually proceed faster if the temperature is increased. Many unstable materials (such as enzymes) will be viable longer at lower temperatures.

Three different scales are commonly used to measure temperature: Fahrenheit (expressed as °F), Celsius (°C), and Kelvin (K). Thermometers measure temperature by using materials that expand or contract when heated or cooled. Mercury or alcohol thermometers, for example, have a reservoir of liquid that expands when heated and contracts when cooled, so the liquid column lengthens or shortens as the temperature of the liquid changes.

## The Fahrenheit Scale

The first thermometers were glass and contained alcohol, which expanded and contracted as the temperature changed. The German scientist, Daniel Gabriel Fahrenheit used mercury in the tube, an idea put forth by Ismael Boulliau. The Fahrenheit scale was first developed in 1724 and tinkered with for some time after that. The main problem with this scale is the arbitrary definitions of temperature. The freezing point of water was defined as $$32^\text{o} \text{F}$$ and the boiling point as $$212^\text{o} \text{F}$$. The Fahrenheit scale is typically not used for scientific purposes.

## The Celsius Scale

The Celsius scale of the metric system is named after Swedish astronomer Anders Celsius (1701 - 1744). The Celsius scale sets the freezing point and boiling point of water at $$0^\text{o} \text{C}$$ and $$100^\text{o} \text{C}$$ respectively. The distance between those two points is divided into 100 equal intervals, each of which is one degree. Another term sometimes used for the Celsius scale is "centigrade" because there are 100 degrees between the freezing and boiling points of water on this scale. However, the preferred term is "Celsius".

## The Kelvin Scale

The Kelvin temperature scale is named after Scottish physicist and mathematician Lord Kelvin (1824 - 1907). It is based on molecular motion, with the temperature of $$0 \: \text{K}$$, also known as absolute zero, being the point where all molecular motion ceases. The freezing point of water on the Kelvin scale is $$273.15 \: \text{K}$$, while the boiling point is $$373.15 \: \text{K}$$. Notice that there is no "degree" used in the temperature designation. Unlike the Fahrenheit and Celsius scales where temperatures are referred to as "degrees $$\text{F}$$" or "degrees $$\text{C}$$", we simply designated temperatures in the Kelvin scale as kelvins.

## Converting between Scales

The Kelvin is the same size as the Celsius degree, so measurements are easily converted from one to the other. The freezing point of water is 0°C = 273.15 K; the boiling point of water is 100°C = 373.15 K. The Kelvin and Celsius scales are related as follows:

$T \,\text{(in °C)} + 273.15 = T \, \text{(in K)} \tag{3.10.1} \label{3.10.1}$

$T \; \text{ (in K)} − 273.15 = T \; \text{(in °C)} \tag{3.10.2} \label{3.10.2}$

Degrees on the Fahrenheit scale, however, are based on an English tradition of using 12 divisions, just as 1 ft = 12 in. The relationship between degrees Fahrenheit and degrees Celsius is as follows: where the coefficient for degrees Fahrenheit is exact. (Some calculators have a function that allows you to convert directly between °F and °C.) There is only one temperature for which the numerical value is the same on both the Fahrenheit and Celsius scales: −40°C = −40°F. The relationship between the scales are as follows:

$°C = \dfrac{5}{9} \times (°F-32) \tag{3.10.3} \label{3.10.3}$

$°F = \dfrac{9}{5} \times (°C)+32 \tag{3.10.4} \label{3.10.4}$

Example $$\PageIndex{1}$$: Temperature Conversions

A student is ill with a temperature of 103.5°F. What is her temperature in °C and K?

SOLUTION

Converting from Fahrenheit to Celsius requires the use of Equation \ref{3.10.3}:

\begin{align} °C &= \dfrac{5}{9} \times (103.5°F - 32) \\ &= 39.7 \,°C\end{align}

Converting from Celsius to Kelvin requires the use of Equation \ref{3.10.1}:

\begin{align} K &= 39.7 \,°C + 273.15 \\ &= 312.9\,K \end{align}

Exercise $$\PageIndex{1}$$

Convert each temperature to °C and °F.

1. the temperature of the surface of the sun (5800 K)
2. the boiling point of gold (3080 K)
3. the boiling point of liquid nitrogen (77.36 K)