8-122
8-168 Liquid water is heated in a chamber by mixing it with superheated steam. For a specified mixing
temperature, the mass flow rate of the steam and the rate of entropy generation are to be determined.
Assumptions 1 This is a steady-flow process since there is no change with time. 2 Kinetic and potential
energy changes are negligible. 3 There are no work interactions.
Properties Noting that T < Tsat @ 200 kPa = 120.21qC, the cold water and the exit mixture streams exist as a
compressed liquid, which can be approximated as a saturated liquid at the given temperature. From Tables
A-4 through A-6,
1200 kJ/min
P1 200 kPa ½ h1 # h f @ 20$ C 83.91 kJ/kg
¾s # s
0.2965 kJ/kg ˜ K
T1 20qC
f @ 20$ C
¿ 1
20qC
1
P2 200 kPa ½ h2 2769.1 kJ/kg
MIXING
2.5 kg/s
¾
CHAMBER
60qC
T2 150qC ¿ s 2 7.2810 kJ/kg ˜ K
3
P3
T3
200 kPa ½ h3 # h f @60$ C 251.18 kJ/kg
¾s # s
0.8313 kJ/kg ˜ K
60qC
f @ 60$ C
¿ 3
2
200 kPa
150qC
Analysis (a) We take the mixing chamber as the system, which is a control volume. The mass and energy
balances for this steady-flow system can be expressed in the rate form as
Mass balance:
m in m out
'm systemÊ0 (steady)
Energy balance:
E E out
in
Rate of net energy transfer
by heat, work, and mass
E in
m 1h1 m 2 h2
0
o m 1 m 2
'E system©0 (steady)
m 3
0
Rate of change in internal, kinetic,
potential, etc. energies
E out
Q out m 3h3
Combining the two relations gives
Q out
m 1h1 m 2 h2 m 1 m 2 h3
m 1 h1 h3 m 2 h2 h3 2 and substituting, the mass flow rate of the superheated steam is determined to be
Solving for m
Also,
m 2
Q out m 1 h1 h3 h2 h3
m 3
m 1 m 2
(1200/60kJ/s) 2.5 kg/s 83.91 251.18kJ/kg
(2769.1 251.18)kJ/kg
0.166 kg/s
2.5 0.166 2.666 kg/s
(b) The rate of total entropy generation during this process is determined by applying the entropy balance
on an extended system that includes the mixing chamber and its immediate surroundings so that the
boundary temperature of the extended system is 25qC at all times. It gives
Sin Sout
Sgen
'Ssystem©0 0
,
Rate of net entropy transfer
by heat and mass
Rate of entropy
generation
m 1s1 m 2 s2 m 3s3 Q out
Sgen
Tb,surr
Rate of change
of entropy
0
Substituting, the rate of entropy generation during this process is determined to be
Q
Sgen m 3s3 m 2 s2 m 1s1 out
Tb,surr
2.666 kg/s 0.8313 kJ/kg ˜ K 0.166 kg/s 7.2810 kJ/kg ˜ K (1200 / 60 kJ/s)
2.5 kg/s 0.2965 kJ/kg ˜ K 298 K
0.333 kW/K
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