Clear[h,  kb, meter, nA, gram, hydrogenMassInAmu, gramsPerAmu, eVinJoules, angstrom, cm]
h = Quantity[1,"PlanckConstant"] ;
meter = Quantity[1,"Meters"]  ;
cm = 0.01 meter ;
gram = Quantity[1,"Grams"] ;
liter = Quantity[1,"Liters"] ;
nA = Quantity[1,"AvogadroNumber"] 
amus = { 
ElementData["Hydrogen", "AtomicWeight"] , ElementData["Helium", "AtomicWeight"] ,
ElementData["Neon", "AtomicWeight"] 
}
hydrogenMassInAmu = amus[[1]] ;
kb = Quantity[1,"BoltzmannConstant"] ;

eVinJoules = (*WolframAlpha["convert 1 electron volt to SI units",{{"Result",1},"ComputableData"}]
*)
Quantity[1.602*^-19,"Joules"]

gramsPerAmu = gram/nA 
masses = amus gramsPerAmu  
massOfHydrogenAtom = masses[[1]] 
angstrom = Quantity[1,"Angstroms"]
bohrRadius = Quantity[1,"BohrRadius"]
hydrogenVolume = 4 Pi bohrRadius^3 /3

bps = {
WolframAlpha["hydrogen boiling point kelvin",{{"Result",1},"ComputableData"},PodStates->{"Result__Show details"}]
,
WolframAlpha["helium boiling point kelvin",{{"Result",1},"ComputableData"},PodStates->{"Result__Show details"}],
WolframAlpha["neon boiling point kelvin",{{"Result",1},"ComputableData"},PodStates->{"Result__Show details"}]} 
hydrogenBoilingPoint =   bps[[1]]

Clear[s, emin]
s[n_, v_, m_, e_] = n kb  (Log[ (v/n) (4 Pi m e/(3 n h^2))^(3/2)] + 5/2) ;
emin[n_, v_, m_] = Solve[ s[n, v,m,e] == 0, e]
emin[nA, cm^3,massOfHydrogenAtom]
emin[1, hydrogenVolume,massOfHydrogenAtom]

(QuantityUnit[0.58047727958785225743072906930627331643`5.442204452320756]) / eVinJoules

Table[
(1 liter)/(10^23) (Sqrt[2 Pi masses[[i]] kb bps[[i]]]/h)^3, {i, 1, 3}]