Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 107

Therefore,

c) At a height we have,from(S.4.19.3),

where weused foruniform acceleration. Now, the maximum force

is defined by

So, assumingthat theaveragetemperature for theisothermalatmosphere

wefind

4.20 Adiabatic Atmosphere (Boston, Maryland)

a) Startingfrom the ideal gas law, we can express thetemperatureTas a

function ofpressurePand the massdensity

wherePand are functions of theheight above thesurface of the Earth:
Taking the derivative ofTwithrespect to we have

We need to express interms ofdP. The fact that is independent
of altitudeallows us towrite

whereBis some constant. So