# UY1: Temperature Scales

(1) The Fahrenheit Scale

– Invented by Gabriel Fahrenheit (1686 – 1736)

– Between 1708 – 1724, he discovered ways to make high quality liquid-in-glass thermometers and proposed the following fixed points to standardise measurements.

Two fixed points:

– Melting point of ice: 32°F

– Boiling point of water: 212°F

(2) The Celsius Scale

– Invented by Anders Celsius (a Swedish astronomer), 1701 – 1744

– After careful experiments, Celsius chose the two fixed points to be the melting point of ice and the boiling point of water.

He assigned values to the two fixed points:

– Melting point of ice: 100°C

– Boiling point of water: 0°C
Celsius then divided the scale into 100 degrees between the two fixed points, and called it the centigrade scale (“centigrade” means 100 steps in Latin). At first, he put the zero at the boiling point of water, and 100 at the melting point of ice.

In 1742, he published a paper “Observations of two persistent degrees on a thermometer” in the Annals of the Royal Swedish Academy Of Science.

Then the fixed points were switched around:

– Melting point of ice: 0°C

– Boiling point of water: 100°C

In 1948, the world body renamed it the Celsius Scale.

Converting between the Fahrenheit and the Celsius Scales

Both Fahrenheit and Celsius scales are linear scales. The equation used to convert between the two is:

$$F = a C + b$$

,where F is Fahrenheit reading, C is Celsius reading, a and b are constants to be determined.

We know that $0^{\circ} \, \text{C}$ is mapped to $32^{\circ} \, \text{F}$ and $100^{\circ} \, \text{C}$ is mapped to $212^{\circ} \, \text{F}$.

Hence,

\begin{aligned} 32 &= a (0) + b \\ 212 &= a(100) + b \end{aligned}

We get $a = 1.8$ and $b = 32$.

$$F = 1.8 C + 32$$
(3) The Kelvin Scale

– This scale is based on the absolute zero of temperature, 0 K (the state of minimum thermal energy) and uses degrees equal in size to the Celsius degree, so it needs only one other fixed point. The standard fixed point adopted is the triple point of water: 273.16K at 4.58 mm of mercury pressure.

The triple point of water is a state at which liquid water, water vapour and ice coexist in equilibrium. It occurs at 273.16K and 4.58 mm mercury pressure.

(4) The Rankine Scale

– This scale is also based on the theoretically absolute zero of temperature but uses degrees equal in size to the Fahrenheit degree. Hence, the freezing point of water is 491.6°R.
Fixed points and other reference points:

Degree Celcius Fahrenheit
helium normal b.p.  -268.935$^{\circ}$C  4.215 K
hydrogen triple point  -259.3467$^{\circ}$C  13.8033 K
neon triple point  -248.5939$^{\circ}$C  24.5561 K
oxygen triple point  -218.7916$^{\circ}$C  54.3584 K
water triple point 0.010$^{\circ}$C  273.16 K

Food For Thought:

In the far future, a group of astronauts visited a planet inhabited by aliens. The aliens have a temperature scaled based on the freezing and boiling points of water, and are separated by 100 of the aliens’ degrees. (What a coincidence) Would the size of the aliens’ degrees be similar to ours? Suppose the aliens have also came up with a scale similar to the Kelvin Scale. Would the absolute zero on their scale be the same as ours?

Answer: The values of 0°C and 100°C for the freezing and boiling points of water are defined at our atmospheric pressure. It is unlikely that the atmospheric pressure on their alien planet would be exactly the same as that on the Earth. Therefore, water would freeze and boil at different temperatures on the alien planet. The aliens may call these temperature 0°A and 100°A, but they would not be the same temperatures as our 0°C and 100°C. If the aliens did assign values of 0°A and 100°A for these temperatures, their degrees would not be the same as ours Celsius degrees (unless their atmospheric pressure is same as ours). For an alien version of the Kelvin scale, the absolute zero would be the same as ours because it is based on a natural, universal definition rather than being associated with a particular substance or a given atmospheric pressure.

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