Temperature Scales and Their Relations

Temperature Scales and Their Relations

A temperature scale is constructed by choosing two fixed points -- physical states that are easily

and reproducibly obtained in a laboratory, each assigned a fixed numerical temperature value by

convention -- and then dividing the interval between them into a chosen number of equal parts, called

degrees.

The Celsius scale

The Celsius scale (once called the centigrade scale) takes the ice point of pure water (the

temperature at which ice and water coexist in equilibrium at standard atmospheric pressure) as its lower

fixed point, assigning it the value $0\,^\circ\text{C}$, and the steam point of pure water (the

temperature at which water boils at standard atmospheric pressure) as its upper fixed point, assigning it

$100\,^\circ\text{C}$. The interval between the two is divided into $100$ equal degrees.

The Fahrenheit scale

The Fahrenheit scale, still used in some everyday, clinical (body temperature), and meteorological

contexts, fixes the very same two physical reference points but assigns them different numbers: the ice

point is $32\,^\circ\text{F}$ and the steam point is $212\,^\circ\text{F}$, so the interval between them

is divided into $212 - 32 = 180$ equal degrees. Because a Fahrenheit degree is a smaller unit than a

Celsius degree ($180$ divisions covering the same physical temperature range as $100$ Celsius divisions),

$1\,^\circ\text{C}$ corresponds to a change of $\dfrac{180}{100} = \dfrac{9}{5}\,^\circ\text{F}$.

The Kelvin (absolute) scale

The Kelvin scale is the SI unit of temperature, and it is fixed in a fundamentally different way: rather

than using the freezing and boiling points of one particular substance (water), it is anchored at

absolute zero ($0\ \text{K}$), the theoretical lower limit of temperature at which, for an ideal gas,

both pressure and volume would fall to zero, and at which molecular motion would (classically) cease

entirely. Each Kelvin degree is chosen to be exactly the same size as a Celsius degree, so that the ice

point of water works out to $273.15\ \text{K}$ (usually rounded to $273\ \text{K}$ for classroom

calculations) and the steam point to $373.15\ \text{K}$ ($373\ \text{K}$).

Converting between the scales

Because all three scales are linear functions of one another, a single set of ratios connects any given

temperature reading on all three simultaneously:

$\frac{C - 0}{100} = \frac{F - 32}{180} = \frac{K - 273}{100}$ …