By Kent W. Mayhew

*Boltzmann’s So-Called Constant & Work*

*N*) are in the thermometer’s glass bulb, and the pressure
(*P*), volume (*V*), and temperature (*T*), then by rearranging the ideal gas law (PV=NkT), *k *can be calculated:

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) similarly implies that Boltzmann’s constant (*k*) defines on a per molecule basis the proportionality for the work required
to displace the overlying Earth’s atmosphere by a height of *dh*, per degree of temperature change.

The above means that Boltzmann’s constant is a function of the Earth’s gravitational field which is to say that it is only really a constant here on Earth. When universally applied it is only a so-called constant.

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