Implications to Statistical Thermodynamics
A fundamental equation to statistical thermodynamics is entropy (S) defined in terms of the number of microstates (@) i.e.
It must be emphasized that eqn 1) is a valid equation because Boltzmannís constant (k) was designed (or if you prefer equated) so that the ideal gas law is valid. That being:
It was similarly designed so that isobaric isothermal lost work equals:
And for the ideal case
The circular issue: There are those who claim that Boltzmannís 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 Boltzmannís constant (k) is a constant valid here on Earth. See Boltzmann Constant Blog
Equally important we must accept that Boltzmannís 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 20th and into the 21st century. This may help the likes of Plank and Mach rest in peace.
Copyright Kent W. Mayhew