By Kent W. Mayhew

**Boltzmann’s So-Called Constant & Work**

k=PV/NT 1)

Consider a unit cube whose volume is “V” with surface
area:” A”. If “M” represents the mass of overlying atmosphere, and “g” is gravitational constant. Then the pressure exerted by the
Earth’s atmosphere on the top surface of the unit cube is:

P=Mg/A 2)

Accordingly,
eqn 1) can be rewritten:

k=(Mg/A)(V/NT) 3)

Remember for a unit cube, then: V/A=h, wherein: “h” is the height of the unit
cube. Therefore we can rewrite 3) as

k=(Mg/T)(h/N) 4)

Which becomes:

kTN=Mgh 5)

Limit the volume change to only vertical expansion, i.e. along the y-axis and then differentiating both sides, we obtain the change
in temperature with height as:

NkdT=Mgdh 6)

Thus:

k=(Mg/N)(dh/dT) 7)

Eqn 7) simiply implies that Boltzmann’s constant (k) defines on a per molecule basis, the proportionality for the work by an
ideal gas that is required to displace the overlying Earth’s atmosphere by a height of dh, per degree of temperature change.

The above implies that Boltzmann’s constant (k) is a function of the Earth’s gravitational field, which is to say that it is only really and truly only a constant here on Earth. When universally applied it is only a so-called constant at best, one too often misused in sunjects like cosmology. This further alienates our new thermodynamics from traditional considerations.

Of course for a mole of gaseous molecules what is said of Boltzmann's constant equally applies to the ideal gas constant (R)

Copyright Kent W. Mayhew

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