Scale of temperature
Scale of temperature is a methodology of calibrating the
Celsius, Kelvin, and Fahrenheit are common temperature scales. Other scales used throughout history include Rankine, Rømer, Newton, Delisle, Réaumur, Gas mark, Leiden and Wedgwood.
Definition
This section may be too technical for most readers to understand.(August 2021) |
The
The second law of thermodynamics provides a fundamental, natural definition of thermodynamic temperature starting with a null point of absolute zero. A scale for thermodynamic temperature is established similarly to the empirical temperature scales, however, needing only one additional fixing point.
Empirical scales
Empirical scales are based on the measurement of physical parameters that express the property of interest to be measured through some formal, most commonly a simple linear, functional relationship. For the measurement of temperature, the formal definition of thermal equilibrium in terms of the thermodynamic coordinate spaces of thermodynamic systems, expressed in the zeroth law of thermodynamics, provides the framework to measure temperature.
All temperature scales, including the modern thermodynamic temperature scale used in the
Different empirical scales may not be compatible with each other, except for small regions of temperature overlap. If an alcohol thermometer and a mercury thermometer have the same two fixed points, namely the freezing and boiling point of water, their readings will not agree with each other except at the fixed points, as the linear 1:1 relationship of expansion between any two thermometric substances may not be guaranteed.
Empirical temperature scales are not reflective of the fundamental, microscopic laws of matter. Temperature is a universal attribute of matter, yet empirical scales map a narrow range onto a scale that is known to have a useful functional form for a particular application. Thus, their range is limited. The working material only exists in a form under certain circumstances, beyond which it no longer can serve as a scale. For example,
Ideal gas scale
When pressure approaches zero, all real gas will behave like ideal gas, that is, pV of a mole of gas relying only on temperature. Therefore, we can design a scale with pV as its argument. Of course any bijective function will do, but for convenience's sake a linear function is the best. Therefore, we define it as[5]
The ideal gas scale is in some sense a "mixed" scale. It relies on the universal properties of gas, a big advance from just a particular substance. But still it is empirical since it puts gas at a special position and thus has limited applicability—at some point no gas can exist. One distinguishing characteristic of ideal gas scale, however, is that it precisely equals thermodynamical scale when it is well defined (see § Equality to ideal gas scale).
International temperature scale of 1990
ITS-90 is designed to represent the thermodynamic temperature scale (referencing absolute zero) as closely as possible throughout its range. Many different thermometer designs are required to cover the entire range. These include helium vapor pressure thermometers, helium gas thermometers, standard platinum resistance thermometers (known as SPRTs, PRTs or Platinum RTDs) and monochromatic radiation thermometers.
Although the Kelvin and Celsius scales are defined using absolute zero (0 K) and the
Thermometers calibrated per ITS–90 use complex mathematical formulas to interpolate between its defined points. ITS–90 specifies rigorous control over variables to ensure reproducibility from lab to lab. For instance, the small effect that atmospheric pressure has upon the various melting points is compensated for (an effect that typically amounts to no more than half a
There are often small differences between measurements calibrated per ITS–90 and thermodynamic temperature. For instance, precise measurements show that the boiling point of
Celsius scale
Celsius (known until 1948 as centigrade) is a temperature scale that is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale two years before his death. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale as well as a unit to indicate a temperature interval (a difference between two temperatures).
From 1744 until 1954, 0 °C was defined as the freezing point of water and 100 °C was defined as the boiling point of water, both at a pressure of one standard atmosphere.[citation needed]
Although these defining correlations are commonly taught in schools today, by international agreement, between 1954 and 2019 the unit degree Celsius and the Celsius scale were defined by absolute zero and the triple point of VSMOW (specially prepared water). This definition also precisely related the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature with symbol K. Absolute zero, the lowest temperature possible, is defined as being exactly 0 K and −273.15 °C. Until 19 May 2019, the temperature of the triple point of water was defined as exactly 273.16 K (0.01 °C). This means that a temperature difference of one degree Celsius and that of one kelvin are exactly the same.
On 20 May 2019, the kelvin was
Thermodynamic scale
Thermodynamic scale differs from empirical scales in that it is absolute. It is based on the fundamental laws of thermodynamics or statistical mechanics instead of some arbitrary chosen working material. Besides it covers full range of temperature and has simple relation with microscopic quantities like the average kinetic energy of particles (see equipartition theorem). In experiments ITS-90 is used to approximate thermodynamic scale due to simpler realization.
Definition
Lord Kelvin devised the thermodynamic scale based on the efficiency of heat engines as shown below:
The efficiency of an engine is the work divided by the heat introduced to the system or
where wcy is the work done per cycle. Thus, the efficiency depends only on qC/qH.
Because of
In addition, a reversible heat engine operating between temperatures T1 and T3 must have the same efficiency as one consisting of two cycles, one between T1 and another (intermediate) temperature T2, and the second between T2 and T3. This can only be the case if
Specializing to the case that is a fixed reference temperature: the temperature of the triple point of water. Then for any T2 and T3,
Therefore, if thermodynamic temperature is defined by
then the function f, viewed as a function of thermodynamic temperature, is
and the reference temperature T1 has the value 273.16. (Of course any reference temperature and any positive numerical value could be used—the choice here corresponds to the Kelvin scale.)
Equality to ideal gas scale
It follows immediately that
Substituting Equation 3 back into Equation 1 gives a relationship for the efficiency in terms of temperature:
This is identical to the efficiency formula for Carnot cycle, which effectively employs the ideal gas scale. This means that the two scales equal numerically at every point.
Conversion table between different temperature scales
See also
Notes and references
- ISBN 978-0-521-04359-5.
- ISBN 978-981-02-4477-4.
- ^ Walter Greiner; Ludwig Neise; Horst Stöcker. Thermodynamics and statistical mechanics. New York [u.a.] : Springer, 2004. pp. 6~7.
- ISBN 978-3-540-85417-3.
- ^ "Thermometers and the Ideal Gas Temperature Scale".