Implications to Statistical Thermodynamics

A fundamental equation to statistical thermodynamics is entropy (S) defined
in terms of the number of microstates (@) i.e.
S=kIn@
1)
It must be emphasized that eqn 1) is a valid equation because Boltzmann’s constant (k) was designed (or if you prefer
equated) so that the ideal gas law is valid. That being:
PV=NkT 2)
It was similarly designed so that isobaric isothermal lost work equals:
W(lost)=TdS=dE+PdV 3)
And for the ideal case
W(lost)=PdV 4)
The circular issue: There are those who claim that Boltzmann’s brilliant mathematic simply proves that traditional
thermodynamics is correct. And of course all the statistical arguments and equations that follow are valid, all then seemingly also
verify the science.
You must understand that designing a math and then having a constant (k) such that the math equals
empirical data is a fundamental aspect of the sciences. However to then claim that since this math now explains that very empirical
data verges upon a circular argument. And this is fundamentally what happened in thermodynamics. Accordingly, those who claim that
statistical thermodynamics proves that traditional interpretations are absolutely correct are delusional.
In
another blog I discuss that Boltzmann’s constant (k) is a constant valid here on Earth. See Boltzmann Constant Blog
Equally important we must accept that Boltzmann’s math was brilliant. However the number of microstates has nothing to do with volume
or randomness. It simple is a relation to the energy within a system. Increase a systems thermal energy and the number of microstates
increase. This will have implications throughout statistical thermodynamics.
Furthermore we must accept how walls influence
all forms of thermodynamics. See Walls Blog
And finally we might need to accept the notion that or world is not defined by probabilities, at least to the extent that this concept has grown throughout the 20^{th} and into the 21^{st} century. This may help the likes of Plank and Mach rest in peace.
Copyright Kent W. Mayhew