Transcript 19-summary.ppt

Chapter 19: The Kinetic Theory of Gases
m mass of one molecule; M is the molar mass; n is the
number of moles; NA is Avogadro’s number; Msam is the
mass of the sample (or system); P: absolute (not gauge!)
pressure; T: absolute (not Celsius!) temperature; R is the
“Universal” gas constant; k = Boltzmann’s constant
NA = 6.02 1023 mol-1
N = n NA
n = Msam/M = n = Msam/(m NA)
R= 8.314 J/(mol K)
k = R/NA = 1.38 10-23 J/K
For an ideal gas [IG],
PV=nRT= N kT
W = n R T ln (Vf/Vi)
W = P DV
[isothermal]
[isobaric]
vrms = (3 R T/M)1/2
P = (n M vrms2)/(3V)
Translation kinetic energy: Kavg = (3/2) k T
Eint = (3/2) n R T
[monatomic IG]
DEint= n cv DT
[for all IG]
cv = (3/2) R = 12.5 J/(mol K)
[monatomic IG]
cp - cv = R
[for all IG]
cp = 20.8 J/(mol K)
[monatomic IG]
Equipartition theorem: For every molecule there is 1/2 kBT
per degree of freedom!
  cp/ cv
 = 5/3 = 1.67
[monatomic IG ]
 = 7/5 = 1.4
[diatomic IG]
For a [reversible] adiabatic process:
p1V1 = p 2 V2
T1 V1 (-1) = T2 V2 (-1)
What about free expansion? It is non-reversible!!!!
Q = 0, W = 0 ; DEint= 0; DT= 0; p V = n R T
p1V 1 = p 2V2
[IG free expansions]