On 15.04.2011 21:44 meekerdb said the following:
Entropy and information are related. In classical thermodynamics the
relation is between what constraint you impose on the substance and
dQ/T. You note that it is calculated assuming constant pressure -
that is a constraint; another is assuming constant energy. In terms
of the phase space in a statistical mechanics model, this is
confining the system to a hypersurface in the the phase space. If you
had more information about the system, e.g. you knew all the
molecules were moving the same direction (as in a rocket exhaust)
that you further reduce the part of phase space and the entropy. If
you knew the proportions of molecular species that would reduce it
further. In rocket exhaust calculations the assumption of fixed
species proportion is often made as an approximation - it's referred
to as a frozen entropy calculation. If the species react that changes
the size of phase space and hence the Boltzmann measure of entropy.
First how do you define information? According to Shannon?
Then if we consider a thermodynamic system, the Second Law
dS >= dQ/T
does not impose constraints as such. It is held for any closed system
and for any process. The only assumption here is that the system
possesses a temperature. If one can define temperature than the entropy
follows according to the Second Law unambiguously and I do not see how
one additionally will need information, whatever it means.
If you speak about reaction chemistry, let us consider a simple exercise
from classical thermodynamics.
Problem. Given temperature, pressure, and initial number of moles of
NH3, N2 and H2, compute the equilibrium composition.
To solve the problem one should find thermodynamic properties of NH3, N2
and H2 for example in the JANAF Tables and then compute the equilibrium
From thermodynamics tables (all values are molar values for the
standard pressure 1 bar, I have omitted the symbol o for simplicity but
it is very important not to forget it):
Del_f_H_298(NH3), S_298(NH3), Cp(NH3), Del_f_H_298(N2), S_298(N2),
Cp(N2), Del_f_H_298(H2), S_298(H2), Cp(H2)
2NH3 = N2 + 3H2
Del_H_r_298 = Del_f_H_298(N2) + 3 Del_f_H_298(H2) - 2 Del_f_H_298(NH3)
Del_S_r_298 = S_298(N2) + 3 S_298(H2) - 2 S_298(NH3)
Del_Cp_r = Cp(N2) + 3 Cp(H2) - 2 Cp(NH3)
To make life simple, I will assume below that Del_Cp_r = 0, but it is
not a big deal to extend the equations to include heat capacities as well.
Del_G_r_T = Del_H_r_298 - T Del_S_r_298
Del_G_r_T = - R T ln Kp
When Kp, total pressure and the initial number of moles are given, it is
rather straightforward to compute equilibrium composition. So, the
entropy is there. What do you mean when you state that information is
also involved? Where is in this example the related information, again
whatever it is?
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