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What is Temperature?


DEFINITION: (For this website usage):

Temperature: A measure proportional to the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules. The flow of heat is from a high temperature region toward a lower temperature region.
-Courtesy of the references cited below but mostly based on the operational definition on the HyperPhysics pages at Georgia State University by R. Nave. and the discussion in "Traceable Temperatures" Second Ed. by Nicholas and White-See the discussions and definitions below for our rationale.


Looking at textbooks and related references and even websites for a definition of temperature can be very frustrating. Many talk around the subject and never get to the point or never state a clear definition. Oh, yes, we can find information about the fact that temperature is not heat and what temperature scales are. We know it's related to heat and there is a difference between them. What is it? It's got to be on the Web.....

Bottom line. It is. However it is like finding the needle in a haystack; just like many topics on the web. Search engines do not help much; it takes digging by someone who understands the subject.

A serious group of experts at The American Society for Testing and Materials (ASTM) publishes standards about devices and information on how to calibrate, test and specify temperature sensors. But their standard on Teminology, ASTM E-344, is notably missing a definition for "Temperature"! Surprise!

Is it just us, or have you, too, noticed that there seems to be a real difficulty in defining or agreeing the meaning of the word and concept of "Temperature".


(Bottom line: It is not a simple concept, despite all the work done on it over the past few hundred years. Yes, it can be defined, but not easily. In many cases simplified explanations, not true definitions, are used. See the HyperPhysics Web site at Georgia State University for the clearest and best explained definition we have seen to date. Their definition appears at the bottom of this page.)

Temperature-Do we know what it is?
Here are some samples of definitions that we have found:

  1. "Temperature is the degree of 'hotness' of a body: more precisely it is the potential for heat transfer. In our everyday lives, we are aware of different temperatures through the sensation of touch, but how hot or cold something feels is subjective. We can say that the kettle is hotter than the ice-cream, but not by how much. Measurement, on the other hand, must be objective and a thermometer is used."
    National Physical Laboratory, Teddington, Middlesex, UK, TW11 0LW Crown Copyright 2001. Reproduced by permission of the Controller of HMSO.

  2. "What is Temperature?"
    "In a qualitative manner, we can describe the temperature of an object as that which determines the sensation of warmth or coldness felt from contact with it. It is easy to demonstrate that when two objects of the same material are placed together (physicists say when they are put in thermal contact), the object with the higher temperature cools while the cooler object becomes warmer until a point is reached after which no more change occurs, and to our senses, they feel the same. When the thermal changes have stopped, we say that the two objects (physicists define them more rigorously as systems) are in thermal equilibrium . We can then define the temperature of the system by saying that the temperature is that quantity which is the same for both systems when they are in thermal equilibrium."
    From The Popular Website "About Temperature" (since 21 Nov 1995).
    "About Temperature" Disponible en espanol
  3. Temperature, when measured in Kelvin degrees, is a number that is directly proportional to the average kinetic energy of the molecules in a substance. So, when the molecules of a substance have a small average kinetic energy, then the temperature of the substance is low.

    From The Physics and Mathematics Web Site "Zona Land"
    NOTE: This website also has an interesting page that graphically illustrates the relationship between molecular motion and the temperature of a gas.

  4. "Temperature can be defined in macroscopic terms, using concepts of thermodynamics, as an intrinsic property of matter that quantifies the ability of one body to transfer thermal energy (heat) to another body..."Temperature can also be defined on a microscopic scale as proportional to the random kinetic energy of an assemblage of molecules or atoms."

    "Industrial Temperature Measurement" T.W Kerlin and R.L. Shepard, The Instrument Society of America, Research Triangle Park, NC, 1982 (ISBN 0-87664-622-4)

  5. "Temperature: A convenient operational definition of temperature is that it is a measure of the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules. The flow of heat is from a high temperature region toward a lower temperature region.

    "The details of the relationship to molecular motion are described in kinetic theory. The temperature defined from kinetic theory is called the kinetic temperature. Temperature is not directly proportional to internal energy since temperature measures only the kinetic energy part of the internal energy, so two objects with the same temperature do not in general have the same internal energy (see water-metal example). Temperatures are measured in one of the three standard temperature scales (Celsius, Kelvin, and Fahrenheit).

    "A More General View of Temperature: When a high temperature object is placed in contact with a low temperature object, then energy will flow from the high temperature object to the lower temperature object, and they will approach an equilibrium temperature.

    "When the details of this common-sense scenario are examined, it becomes evident that the simple view of temperature embodied in the commonly used kinetic temperature approach has some significant problems.

    "The above illustration summarizes the situation when the kinetic temperature gives a reasonable general description of the nature of temperature. For monoatomic gases acting like point masses, a higher temperature simply implies higher average kinetic energy. Faster molecules striking slower ones at the boundary in elastic collisions will increase the velocity of the slower ones and decrease the velocity of the faster ones, transferring energy from the higher temperature to the lower temperature region.

    "With time, the molecules in the two regions approach the same average kinetic energy (same temperature) and in this condition of thermal equilibrium there is no longer any net transfer of energy from one object to the other. The concept of temperature is complicated by internal degrees of freedom like molecular rotation and vibration and by the existence of internal interactions in solid materials which can include collective modes.

    " The internal motions of molecules affect the specific heats of gases, with diatomic hydrogen being the classic case. Collective modes affect the specific heats of solids, particularly at low temperatures. Complications such as these have led to the adoption of a different approach to the concept of temperature in the study of thermodynamics.

    "Schroeder's proposal for a theoretical definition of temperature is:
    "* Temperature is a measure of the tendency of an object to spontaneously give up energy to its surroundings. When two objects are in thermal contact, the one that tends to spontaneously lose energy is at the higher temperature."(Thermal Physics, Ch 1.)

    "The kinetic temperature for monoatomic ideal gases described above is consistent with this definition of temperature for the simple systems to which it applies. In that case the equilibrium reached is one of maximum entropy, and the rate of approach to that state will be proportional to the difference in temperature between the two parts of the system. Noting that the equilibrium state of a collection of particles will be the state of greatest multiplicity, then one can define the temperature in terms of that multiplicity (entropy) as follows:

    "Temperature is expressed as the inverse of the rate of change of entropy with internal energy, with volume V and number of particles N held constant. This is certainly not as intuitive as molecular kinetic energy, but in thermodynamic applications it is more reliable and more general."

    From the website HyperPhysics at Georgia State Univerity, author R. Nave.

  6. "For most materials, temperature can be considered to be a measure of the density of heat in a body."...

    "Kelvin was also able to show that this definition (The ratio of heat taken in at a high temperature to the heat taken out at a lower temperature for an ideal, Carnot, heat engine depends on the ratio of a function of the temperatures) leads to an equation for ideal gases of the form

    PV=constant xT

    so that Kelvin's definition of temperature is equivalent to the the gas scale originally proposed by Amontons, and implemented by Chappuis in 1889.....

    "When applied to an ideal box they obtained (by considering a material model based on the movement and collisions of individual atoms in a closed box, Kelvin and others were able to show that thermal equilibrium requires the mean kinetic energy of the atoms to be the same) the result

    PV= constant x (mv^2/2)

    where (mv^2/2) is the average kinetic energy of each atom in the gas. Comparison of this equation with Equation (1.3) (the previous equation) shows that the temperature is proportional to the average kinetic energy of each atom...."Note that the total kinetic energy of molecular gases is higher than that for monatomic gases because they can rotate and vibrate; in that case the temperature is proportional to the mean translational kinetic energy."

  7. "Traceable Temperatures" Second Edition, by J. V. Nicholas and D. R. White, John Wiley & Sons, LTD, Chichester, 2001
    ISBN 0-471-49291-4 .

SUMMARY:
Temperature can be defined in several ways, many of which are not completly accurate, but the first definition of Number 5, above, seems to almost fit our understanding and work reasonably well as an "Operational Definition" for the term. However, the detail provided in the last reference (Number 6) gives a more complete understanding and shows that the word "proportional" really belongs in the definition. At least that's the opinion of this website editor and publisher.

If you have another view, please let us know and, if it is persuasive, we will post here also. Just feedback on our special website for feedback and commentary.

 

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