416 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th9-1.pm5

Also m = Σ mi [from eqn. (9.3)]

∴

pV

RT

=

pV

RT

i

∑ i

∴

p

R

=

p

R

i

i

∑

Using the relation R =

R

M

(^0) , and substituting, we have
pM
R 0

pM
R
ii
0
∑
or pM = ∑piMi
i.e., M =
p
p
∑ iMi ...(9.15)
Now using eqn. (9.14), we have
M =
V
V
∑ iMi ...(9.16)
and M =
n
n
∑ iMi ...(9.17)
Alternately
p = Σ pi = pA + pB + ...... pi
Also pV = mRT
Similarly pAV = mARAT
pBV = mBRBT
∴ pV = pAV + pBV + ......
or mRT = mARAT + mBRBT + ......
∴ mR = mARA + mBRB + ......
But R =
R
M
(^0) , R
A =
R
MA
(^0) , R
2 =
R
MB
0
Substituting this in the above equation, we get
m
R
M
(^0) = m
A^
R
MA
(^0) + m
B^
R
MB
(^0) + ......
∴
1
M

m
mM
m
mM
A
A
B
B
..^11 + + ......

m
M
m
M
fA
A
fB
B

• 
  
  
  
  • 
    

    ......
    where mfA, mfB etc. are the mass fractions of the constituents.
    ∴^1
    M

    
    

    m
    M
    fi
    i
    ∑
    ∴ M =^1 m
    M
    fi
    ∑ i
    ...(9.18)