From owner-biophysics@net.bio.net Sun Feb 15 22:00:00 1998 Path: biosci!bcm.tmc.edu!news.msfc.nasa.gov!newsfeed.internetmci.com!206.229.87.25!news-peer.sprintlink.net!news.sprintlink.net!Sprint!worldnet.att.net!news.u.washington.edu!fujimoto From: fujimoto@u.washington.edu (Bryant Fujimoto) Newsgroups: bionet.biophysics Subject: Re: Boltzmann's vs. thermodynamic entropy Date: 16 Feb 1998 09:23:48 GMT Organization: University of Washington Lines: 60 Distribution: bionet Message-ID: <6c90j4$mkj$1@nntp3.u.washington.edu> References: <6c43le$hr7@mserv1.dl.ac.uk> NNTP-Posting-Host: homer11.u.washington.edu X-Trace: nntp3.u.washington.edu 887621028 23187 (None) 140.142.64.4 X-Complaints-To: help@cac.washington.edu NNTP-Posting-User: fujimoto Pentcho Valev writes: >I wrote: >>So I >>hope you would agree with the following answer: If systems can >>spontaneously move from a more probable to a less probable state, the two >>entropies coincide. If not, not. >Bryant Fujimoto replied:>>>>>>>>>>>> >I don't remember how you came to conclude this, but its incorrect.<<<<<<< >Let me remind you. Consider the following system: >--------------------------------------------------------------------------- > A + B <-> C + D >---------membrane-permeable-only-to-D-------------------------------------- > D >------------------------piston-------------------------------------------- >This is a semi-grand ensemble: The EXOTHERMIC gas reaction A + B <-> C + D >undergoes an isothermal reversible course as D in the lower compartment >pushes a piston and expands. As heat is released by the system, the >thermodynamic entropy of the system DECREASES. On the other hand, this >reversible course has its spontaneous conterpart (D can expand irreversibly, >without pushing the piston). If, in the spontaneous process, the system >moves to a MORE probable state, Boltzmann's entropy INCREASES and does not >coincide with the thermodynamic entropy. If, in the spontaneous process, >the system moves to a LESS probable state (some people claimed so), >Boltzmann's entropy decreases, like the thermodynamic entropy. >As you can see, the problem is real and quite independent of my >personality. What does your personality have to do with this? I certainly haven't referred to it. Do you want me to? If so, why? It is possible to use thermodynamics to determine the entropy of both the initial and final states, without having to worry about whether the process you wish to use is reversible. Since comparisons of these sorts of calculations with calculations of statistical mechanics yield good agreement, what is the problem? The fact is that, experimental results contradict your assertion. Until you can point to an actual reaction, which behaves the way you think it will, you have nothing comparable. Keep in mind, your system is undergoing an isothermal expansion. If you simply expand a non-reacting gas isothermally, heat will flow _into_ the system. So, how do you know that your exothermal reaction will give off more heat than is necessary to keep the temperature constant due to the expansion? You haven't named the reaction, and until you can, you don't have a demonstration of anything. Regards, Bryant P.S. What does thermodynamics mean by reversible? .