GASES AND VAPOUR MIXTURES 429

dharm

\M-therm\Th9-2.pm5

xCO 2 =

6

44

4

28

6

44

+

=

01364

01428 01364

.

..+

= 0.488. (Ans.)

(ii)The equivalent molecular weight of the mixture, M :

M = 0.511 × 28 + 0.488 × 44 = 35.78 kg/kg mole. (Ans.)

(iii)The equivalent gas constant of the mixture, Rmix :

Total mass, m = mN 2 + mCO 2 = 4 + 6 = 10 kg

∴ Rmix =

mR m R

m

N 22 N + CO2 2CO

=

4 8 314

28

6 8 314

44

10

×F

HG

I

KJ

+×F

HG

I

KJ

..

Q R R

M

L =

NM

O

QP

0

= 0.232 kJ/kg K. (Ans.)

(iv)The partial pressures and partial volumes :

PN 2 = xN 2 × p = 0.511 × 4 = 2.044 bar. (Ans.)

PCO 2 = xCO 2 × p = 0.488 × 4 = 1.952 bar. (Ans.)

VN 2 =

mRT

p

NN (^22) =^4
8 314
28
293 10
410
3
5
×××
×
.
= 0.87 m^3. (Ans.)
VCO 2 =
mRT
p
CO 22 CO =^6
8 314
44
293 10
410
3
5
×××
×
.
= 0.83 m^3. (Ans.)
(v)The volume and density of the mixture :
Total volume of the mixture,
V =
mRT
p

mRT
p
NN
N
22
2

mRT
p
CO CO
CO
22
2
∴ V = 10 0 232 293 10
410
3
5
×××
×
. = 1.699 m (^3). (Ans.)
Density of the mixture,
ρmix = ρN 2 + ρCO 2 =
m
V

10
6991.
= 5.88 kg/m^3. (Ans.)
(vi)cp and cv of the mixture :
cpN 2 – cvN 2 = RN 2
∴ cvN 2 =
RN 2
γ− 1

8 314
28 1 4 1
.
(.− ) = 0.742 kJ/kg K.
and cpN 2 = 1.4 × 0.742 = 1.039 kJ/kg K