gas law comments
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Short comments dated 6.26.12 by Phil on the ideal gas law. They derive pV = NkT from Reif's stat mech, define the gas constant R = Na k, and convert to the density form p = ρR'T with a specific gas constant R/M, matching Lai's usage on p 389. They end with heat capacities per mole versus per mass, giving cp - cv = R/M, checked against Lai p 392 and Wikipedia.
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Extracted text (machine-read; may contain errors)
Gas Law Comments PhL 6.26.12
The simple gas law is derived in several places in my experience.
1. Using stat mech, Baby Reif derives the law on page 172 as
pV = NkT or p = nkT
where k is Boltzmann's constant, n is the number of molecules per volume, p is mean pressure. One then defines R as
R = Nak Na = Avagadro = number of molecules in a mole of gas
where a mole of gas weighs 28 grams for N2, and ν = number of moles of gas in a container.
N = νNa pV = νNakT = νRT // Boyle's Law, BR p 174 (93)
No doubt this was first an experimental observation and later computed from stat mech. Now
ν/V = moles per unit volume 1 mole weighs M grams where M is the molecular weight.
ρ = mass/volume = Mν/V ν = ρV/M
then we can write
pV = νRT = (ρV/M)RT => p = (1/M) ρRT = ρR'T R' = R/A
and this last is the way things appear in Lai p 389, so he is using an adjusted gas constant.
Wiki http://en.wikipedia.org/wiki/Ideal_gas_law agrees with me, saying
M = the molar mass (grams per mole).
Wiki goes on to define Rspecific = R/M and then they write
This then is what the R means in Lai p 389.
What about specific heats? Wiki http://en.wikipedia.org/wiki/Heat_capacity defines
C = Q/ΔT // for some object
It can be expressed per kg, or per mole. Later this page says
R = "universal gas constant" = Nak
Now I suppose these are heat capacities per mole. If you wanted them per mass, you would do
Cp,m = M cp
Then you would have
cp - cv = R/M = Rspecific // and this agrees with Lai p 392.