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Re: conservation of momentum (was Re: Heat as an indestructiblesubstance)



1) Yes, this is applicable to the thermodynamics of more than just ideal
gases.
2,3) The state function describes equilibrium states (at least in
equilibrium thermo - which is all I know). However if the system is not
in equilibrium (e.g. because of an internal constraint such as a
separating wall) the state (and state function E) to which the system will
settle when the constraint is removed exists and is predictable - this
prediction is in fact the major task of thermodynamics.
4) Yes, the term TdS represents the heat transfer dQrev.
5,6) The state function E(S,N,X) can be inverted to display the state
functions S(E,N,X) or N(E,S,X) or X(E,S,N).
7) For a typical gas, the N's might represent various chemical specie mole
numbers; in a star the N's may represent neutrons, protons, and
electrons. In general N describes entities whose number will change E,
while holding the other state variables constant.
8) e.g. Volume, Electric/Magnetic Polarizations
9, etc) For a multi-variable function (e.g. f(x,y, ...) ) the partial
derivative df/dx is defined to involve the change df which occurs when
only the variable x is changed and the other variables (y...) are held
constant. This is a mathematical operation and is defined irrespective of
whether such constraints exist in a given physical process.

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Pentcho Valev" <pvalev@BAS.BG>
To: <PHYS-L@lists.nau.edu>
Sent: Saturday, May 10, 2003 3:19 AM
Subject: Re: conservation of momentum (was Re: Heat as an
indestructiblesubstance)


| Bob Sciamanda wrote:
|
| > I assume your "either" was meant to be "neither" : )
| >
| > The FLT axiomizes that there exists a system energy state function
| > E(S,N,X). S is the entropy, N is the particle number, and X may be
one or
| > several other state variables. The increment in energy may then be
| > expressed in terms of these state variables and the respective partial
| > derivatives:
| > dE = TdS + MdN + YdX. T, M and Y being the appropriate partial
| > derivatives.
|
| Does this apply to systems different from an ideal gas? Should the
system be
| in equilibrium? If not, how do you define the entropy for a
non-equilibrium
| system? Could your definition be related to the classical definition
| dS=dQrev/T? Is the entropy a state function? Proof? What is N in a
complex
| system containing e.g. biopolymers? Which are the "several other state
| variables" for a complex system? Are you right to write dE = TdS + MdN +
YdX
| if the variables (S, N and X) are not independent? Are they independent?
What
| is the meaning of the partial derivatives if the variables are not
| independent? What is the meaning of the partial derivatives if the
system is
| not at equilibrium?
|
| Pentcho