# 11.1.2 The Kelvin Scale

The first “circumstantial evidence” of the existence of an absolute zero temperature was provided in 1808 by the discovery of the pressure law: for a given mass of ideal gas, the pressure exerted by the gas increases linearly with its temperature, if the volume is kept constant. In fact, constant-volume gas thermometers were the gold standard for temperature calibration in those times. Plotting the pressure vs temperature graphs for different types of gases (e.g. He, H2, O2, N2 etc), every gas yields a straight-line graph

By extrapolating the lines leftward (towards low temperatures that was not attainable physically in the laboratory[1]), one could obtain the theoretical temperature at which the pressure of a gas hypothetically hits zero. This temperature turned out to be -273.15°C, for each and every gas (hydrogen, nitrogen, oxygen, etc)! Naturally, this was speculated to be the absolute zero temperature, the coldest possible temperature at which all molecular motion ceases[2].

Kelvin Scale

1848, the great Scottish physicist Lord Kelvin published a paper titled “On an Absolute Thermometric Scale” in which he pointed out that the principle of the Carnot Cycle[3] can be used as the basis for a thermodynamics scale of temperature that is universal and independent of any property of any particular substance. He also proposed that the absolute zero temperature be assigned the value of zero degree on this proposed scale. This scale is now known as the Kelvin scale. It is a departure from empirical scales because it is based on the laws of thermodynamic which applies to all materials. It is also an absolute scale because it starts from 0 K which is the absolute zero temperature.

For convenience, the interval of one Kelvin (K) is chosen to match the interval of one degree centigrade (°C). With the lowest temperature (what used to be −273.15 °C on the centrigrad scale) anchored at 0 K, the ice and steam points corresponds to 273.15 K and 373.15 respectively.

Celsius Scale

Using such big numbers for everyday life temperatures can be cumbersome if not befuddling. (Imagine 313 K for having a fever and 270 K for a winter day.) For this reason, the Celsius scale was launched. The Celsius scale inherits the °C symbol of the centigrade scale. By design, the temperature in Celsius q is related to the temperature in kelvin T by

$\theta =T-273.15$

Coming full circle, ice continues to melt at 0°C and water continues to boil at 100°C. But the reincarnation of the centigrade scale as the Celsius scale marks the transition from empirical to thermodynamic scale. And the confirmation of the absolute zero temperature truly represents a huge advancement in the field of thermodynamics.

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Concept Test

1604

[1] Note also that most gases liquefy or stop behaving as ideal gases long before this temperature is reached.

[2] Later when it was understood that zero motion is physically impossible (because of quantum physics considerations), the absolute zero temperature came to be understood as the temperature of minimum (not zero) molecular motion.

[3] Just briefly, the Carnot Cycle is a theoretical ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824. It shows that the efficiency of all reversible heat engines operating between two heat reservoirs depends only on the temperatures of the reservoirs, regardless of the working fluid.