13-56
13-76 Two mass streams of two different ideal gases are mixed in a steady-flow chamber while receiving energy by heat
transfer from the surroundings. Expressions for the final temperature and the exit volume flow rate are to be obtained and
two special cases are to be evaluated.
Assumptions Kinetic and potential energy changes are negligible.
Analysis (a) Mass and Energy Balances for the mixing process:
m 1  m 2  m 3
m 1h1  m 2 h2  Q in  m 3h3
1
Steady-flow
chamber
h  C PT
2
m 1CP , 1T1  m 2CP , 2T2  Q in  m 3CP , mT3
CP , m 
T3 
Q in
m 1
m
CP , 1  2 CP , 2
m 3
m 3
m 1CP , 1
m 3CP , m
T1 
m 2CP , 2
m 3CP , m
3
Surroundings
T2 
Q in
m 3CP , m
(b) The expression for the exit volume flow rate is obtained as follows:
RT
V3  m 3v3  m 3 3 3
P3
 m 1CP , 1
m 2CP , 2
Q in 
T1 
T2 


m 3CP , m
m 3CP , m 
 m 3CP , m
CP , 1 R3 m 1 R1T1 CP , 2 R3 m 2 R2T2 R3Q in


V3 
CP , m R1 P3
CP , m R2 P3
P3CP , m
m R
V3  3 3
P3
P3  P1  P2
CP , 1 R3  CP , 2 R3 
R Q
V3 
V1 
V2  3 in
CP , m R1
CP , m R2
P3CP , m
R3 Ru M 1 M 1
R3 M 2
,



R1 M 3 Ru M 3
R2 M 3
CP , 1M 1
CP , 2 M 2
Ru Q in
V3 
V1 
V2 
CP , m M 3
CP , m M 3
P3 M 3CP , m
R
Ru
,
M
The mixture molar mass M3 is found as follows:
M 3   yi M i ,
(c) For adiabatic mixing
V3 
CP , 1M 1
CP , m M 3
yi 
m fi / M i
m
fi
/ Mi
, m fi 
m i
 m i
Q in is zero, and the mixture volume flow rate becomes
V1 
CP , 2 M 2
CP , m M 3
V2
(d) When adiabatically mixing the same two ideal gases, the mixture volume flow rate becomes
M 3  M1  M 2
CP ,3  CP ,1  CP , 2
V3  V1  V2
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