Untitled - Aerobib - Universidad Politécnica de Madrid

12 CHAPTER 1. THERMOCHEMISTRY
Between these magnitudes the following relations exist
∑
c j =c , (1.27)
j
∑
X j =1 . (1.28)
j
Let ρ be the density of the mixture, ρ i the partial density of species A i , Y i its
mass fraction and M i its molar mass. The following relations exist
ρ i = ρY i , (1.29)
∑ ∑
ρ j = ρ, Y j = 1 , (1.30)
j
j
c i = ρ M i
Y i , (1.31)
c = ρ ∑ j
Y j
M j
, (1.32)
The mean molar mass M m of the mixture is defined by
X i = ∑
Y i/M i
, (1.33)
Y j /M j
j
Y i = ∑
M iX i
. (1.34)
M j X j
j
M m = ∑ j
M j X j . (1.35)
From Eqs.
following expression
(1.30) and (1.35) one deduces for M m as a function of Y i the
1
M m
= ∑ j
Y j
M j
. (1.36)
Equation of state of the mixture
Since the number of moles of the mixture per unit volume is c, one has
p = cRT = RT ∑ j
c j = ∑ j
p j , (1.37)
where
p j = c j RT = R gj T = X j p (1.38)