Thermodynamics, Statistical Physics, and Quantum Mechanics

108 SOLUTIONS

Substituting (S.4.20.3) into (S.4.20.2), we obtain

Assuming that theacceleration ofgravity is constant, using the hydrostatic

pressureformula

and substituting(S.4.20.5) into(S.4.20.4), wecan write

b) For the atmosphere,usingdiatomicmolecules with and

we havefrom(S.4.20.6),

This value of isabout a factor of 2 larger than that for theactual

atmosphere.

4.21 Atmospheric Energy (Rutgers)

a) Again startingwith theideal gas law

we have

b) The gravitationalenergy of aslice ofatmosphere ofcrosssectionAand
thickness at a height is simply

while the internalenergy of thesame slice is