From owner-biophysics@net.bio.net Tue Apr 19 23:00:00 1994 Path: biosci!daresbury!trane.uninett.no!sunic!EU.net!howland.reston.ans.net!cs.utexas.edu!swrinde!news.uh.edu!jetson.uh.edu!schieber From: schieber@jetson.uh.edu (Schieber, Jay D.) Newsgroups: bionet.biophysics Subject: Re: Discussion: What is "temperature"? Date: 19 Apr 1994 21:36 CDT Organization: University of Houston Lines: 58 Distribution: world Message-ID: <19APR199421362268@jetson.uh.edu> References: NNTP-Posting-Host: jane.uh.edu News-Software: VAX/VMS VNEWS 1.41 In article , runsun@bilbo.bio.purdue.edu writes... >Don't know if this is the right group to ask this simple question ( I hope the >answer will be simple too): What is "temperature" ? > >It is a term we use more often than any others. When you put your finger into >a cup of water of 95C, you feel hot (I hope so). What do you really "feel"? >Temperature? What does that mean? There must be something different for >that cup of water (let say, cup A) compared to cup B with temp = 50C. Molecular >movement? Vibrational displacement? What cause(s) that? Internal energy? Or, >just "energy state"? Is there any term that we can use to represent this >state, just like that we use "Pressure" and "volume" for two different aspects >of a system? What is the relationship between this term and the "temperature"? > >I've been thinking this problem for some time and, to my knowledge, there >isn't any text book or articles talking about the inside world of >"temperature". For unknown reason I am not satisfied with the present >definition of temperature at all. Any idea? Or, any suggestion of reading is >also welcome. > >Run-Sun Pan >Biological Science, Purdue Univ. >runsun@bilbo.bio.purdue.edu The answer to your question lies in the field of thermodynamics. Temperature is defined as (dU/dS)_V, which is the rate of change of internal energy with respect to entropy at constant volume. Now, you ask, how are internal energy and entropy defined? Well, thermodynamics makes the postulate that there is a thing called internal energy that is a state variable, and is a function of only three things: entropy, volume, and number of moles. It also postulates that this functional form obeys a few simple rules of extensibility, and other simple mathematical properties. It also postulates that you can change the internal energy of an object or continuum by doing work on it, or adding heat to it. Note that the field of thermodynamics does not define internal energy, but just postulates its existence. It is clearly motivated by the idea that on a microscopic scale, molecules have motions, and potentials, and therefore store some energy. The justification for the postulates comes only a posteriori, since it can describe all of the data that exist, and the kind of experiences you mention above. If you would like to get into the "inside world of temperature", as you call it, you should understand the work of Ludwig Boltzmann and Josiah Willard Gibbs. They make the connection between molecules and macroscopic quantities like temperature, pressure and internal energy. This work is over 100 years old, and there has been a great deal of work since then. For fundamental textbooks in this area, I would recommend that by Herb Callen, and that by David Chandler. There may be more basic textbooks, but those are usually unsatisfactory because they are oversimplifications. Jay Schieber > .