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# Why is the difference between Celsius and Kelvin temperatures 273 units?

John 10/13/00

 Vocabulary absolute temperature absolute zero Celsius heat kelvin phase second law of thermodynamics SI temperature thermodynamic temperature triple point universal gas law constant work
According to NIST's Historical Perspective on SI, in 1954 the SI unit for temperature was defined as exactly 1/273.16 of the thermodynamic temperature of the triple point of water. This unit was officially named the "kelvin" (with symbol "K") in 1967.

What's a thermodynamic temperature? A thermodynamic temperature scale is consistent with all laws of thermodynamics. As the "true" temperature scale, the thermodynamic temperature scale is independent of the properties of any particular substance. This requirement is important for high-accuracy temperature measurements. For example, the temperatures read from a mercury thermometer and an alcohol thermometer don't quite agree with each other. The trouble is that the rate at which liquid volume changes with temperature isn't a constant- at higher temperatures, the liquids expand more per degree temperature rise than they do at lower temperatures. The degree marks would have to be placed farther apart on the barrel of the thermometer for higher temperatures than for lower ones. The degree spacing would also depend on the liquid used to fill the thermometer.

How are thermodynamic temperature scales defined? One solution to the problem of defining a substance-independent temperature scale came from theoretical studies of heat engines. The maximum efficiency for converting heat into work using a heat engine is equal to 1 - T/Thot, where the heat engine draws heat from a source at temperature Thot and dumps heat to a cold sink at temperature T.

Lord Kelvin defined the first thermodynamic temperature scale as follows:

T = (1 - e) Thot

where e is the maximum efficiency of the heat engine. The engine can't be more than 100% efficient (e=1), so the lowest temperature possible should be zero on this scale. The committee responsible for maintaining the SI used Kelvin's definition to develop an international temperature scale. When one of the temperatures is fixed at 273.16 K, the other is the thermodynamic temperature in kelvins.

Why choose the "triple point of water" as a reference point? At a temperature of exactly 273.16 K, and a pressure of about 610.5 Pa, the solid, liquid, and gaseous forms of water are at equilibrium. This set of conditions is called a "triple point" because at this point three phases can coexist indefinitely. Even a tiny change in temperature and/or pressure from these values will cause one of the phases to disappear, so it's easy to tell when you have a temperature of exactly 273.16 K and when you don't.

Why do you add 273.15 to convert Celsius to Kelvin, then? Why not 273.16? Because the Celsius scale uses the "ice point" (the point at which liquid water and ice can coexist indefinitely) as its reference point, not the triple point. The ice point is 0.01°C below the triple point of water. By definition, Celsius degrees and kelvins are exactly the same size, so absolute zero is -273.15°C.

Basic Unit Definitions: The Kelvin (NIST)
 Milestones leading to the 1990 International Temperature Scale. Links identify the international committees responsible for maintaining the International System of Units (SI).http://physics.nist.gov/cuu/Units/kelvin.html (10/13/00)

Calibration of Liquid-in-glass Thermometers (NIST)
 Jaquelyn Wise of NIST's Thermometry Group explains the procedure for recalibrating liquid-in-glass thermometers. Adobe Acrobat plugin required.http://www.cstl.nist.gov/div836/836.05/Thermometry%20site/Papers/Lig_recal.pdf (10/13/00)

Lord Kelvin
 A brief bio of Lord Kelvin (William Thomson), with a portrait.http://www.phy.bg.ac.yu/web_projects/giants/kelvin.html (10/13/00)

The Origin of the Celsius Temperature Scale (Johan and Ann Santesson)
 A summary of Anders Celsius's 1742 paper "Observations on two persistent degrees on a thermometer", which describes the rationale and origins of the Celsius temperature scale.http://www.santesson.com/engtemp.html (11/14/98, 10/13/00)

Author: Fred Senese senese@antoine.frostburg.edu

General Chemistry Online! Why is the difference between Celsius and Kelvin temperatures 273 units?