Re: state variables

biplabbose@xxxxxxxxx wrote:
> Hi every one
> In classical thermodynamics the four state variables are P, V, T and
> composition. These are quite obvious for a system of Gases. However
> what are the state variables for any non-gas system. For example, in
> cases interaction between proteins or between protein and DNA.

In general, the thermodynamic variables correspond to the possible ways
extracting or performing mechanical (or chemical) work on the system,
plus either entropy or temperature. The latter must always be included
to account for energy transfered through other than macroscopic
mechanical work or change in the number of particles.

The variables that you listed for the gas are familiar ones, but not
really independent. P and V cannot both be specified at the same time,
since they are thermodynamically conjugate (one corresponds to the work
needed to change the other by a given amount). To completely describe
the thermodynamic state, one needs to specify S, V, and N. Other sets
of state variables can be obtained by replacing any of the three by the
corresponding thermodynamic conjugate, respectively T, p, or mu.

As I said before, each of these variables corresponds to a means of
transfering energy from or to the system. The volume V corresponds to
mechanical compression or expansion of the gas. N corresponds to the
chemical energy of the system which can be changed by changing the
number of particles. And S corresponds to heat transfer, i.e. energy
that cannot be accessed by any other means.

For example, for an elastic solid, there is more than one way for it to
expand or to be compressed. So its volume alone is not an adequate
measure of how mechanical work can be performed on it. That's why one
introduces the elastic displacement tensor and the stress tensor which
is conjugate to it. Other examples include the polarization of
dielectrics which is conjugate to the electric field and magnetization
which is conjugate to the magnetic field.

Coming back to the example you seem to be interested in, a mixture of
interacting (reacting?) proteins and DNA. Since you have different
species of molecules which may undergo chemical reactions, you must
include their respective concentrations as state variables. Other than
that, as long as you can approximate the mixture as a homogeneous fluid
which is neither polarizable nor magnetizable (or equivalently with no
external electric or magnetic fields), your options for other state
variables are basically cut down to the same as the ideal gas.

What may be special about these organic molecules is that they have
extended shapes and their individual rotations may carry some overall
angular momentum, which will couple to the rate of rotation of the
fluid. But I don't think you'll see anything like this.

One more generalization you can introduce in the thermodynamics of
continua is the notion of local equilibrium. Any given fluid or solid
element of the system may be in equilibrium, while neighboring ones are
not. Strictly speaking, in this case the system is not in equilibrium,
but it can be assumed to be quasistatic if the global equilibration
time is much larger than the time scale you are interested in. So the
thermodynamic formalism will still apply. The only change necessary
will be the introduction of position dependence in all the state
variables.

Hope this helps.

Igor

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