Thermodynamics, Statistical Physics, and Quantum Mechanics

(^164) SOLUTIONS
At the critical point, so(S.4.58.3) becomes
For (S.4.58.4) tohold forarbitrary wehave
See Landauand Lifshitz,Statistical Physics, Sect. 153 forfurtherdiscus-
sion.
Hydrogen Sublimation in Intergalactic Space
(Princeton)
Using the Clausius–Clapeyron equation derived in Problem 4.57, we can
estimate thevapor pressure Pat Namely,
where is thenumberdensity, is theaverage speed, and is asticking
coefficient,which forthisestimate we take equal to 1. Here we used the
result of Problem4.14,where wecalculated therate ofparticlesstriking the
surface. Now ifthe density is not toohigh, thenumber ofparticles leaving
the surfacedoes not depend onwhether there isvaporoutside, sothis would
4.59
where is thepressure at thetriple point andRis the gas constant. Here
we disregard thevolume permolecule ofsolidhydrogencompared to the one
for its vapor. Thisformula is written under theassumption that the latent
heat does notdepend on thetemperature, but for anorder-of-magnitude
estimate this is good enough.
Consider solidhydrogen at equilibriumwith itsvapor. Then thenumber
of particles evaporating from the surfaceequals thenumber ofparticles
striking thesurface and sticking to itfrom thevapor. Therate of the
particlesstriking the surface is given by