6-61 qC, the minimum mass flow rate of the cooling water... cooling water is not to exceed 10

6-84 Steam is condensed by cooling water in the condenser of a power plant. If the temperature rise of the
cooling water is not to exceed 10qC, the minimum mass flow rate of the cooling water required is to be
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. 4 Heat loss from the device to the
surroundings is negligible and thus heat transfer from the hot fluid is equal to the heat transfer to the cold
fluid. 5 Liquid water is an incompressible substance with constant specific heats at room temperature.
Properties The cooling water exists as compressed liquid at both states, and its specific heat at room
temperature is c = 4.18 kJ/kg·°C (Table A-3). The enthalpies of the steam at the inlet and the exit states are
(Tables A-5 and A-6)
20 kPa ½
¾ h3
h f x3h fg
251.42 0.95 u 2357.5
20 kPa ½
¾ h4 # hf @ 20 kPa
sat. liquid ¿
2491.1 kJ/kg
251.42 kJ/kg
Analysis We take the heat exchanger 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 (for each fluid stream):
m in m out
m in
m 1
'm system Ê0 (steady)
m out
m 2 m w and
m 3
20 kPa
m 4
m s
Energy balance (for the heat exchanger):
E E out
Rate of net energy transfer
by heat, work, and mass
E in
m 1h1 m 3h3
'E systemÊ0 (steady)
Rate of change in internal, kinetic,
potential, etc. energies
E out
m 2 h2 m 4 h4 (since Q
'ke # 'pe # 0)
Combining the two,
m w h2 h1 m s h3 h4 w :
Solving for m
m w
h3 h 4
h3 h4
m s #
m s
h2 h1
c p T2 T1 Substituting,
m w
(2491.1 251.42)kJ/kg
(4.18 kJ/kg˜ $ C)(10qC)
(20,000/3600 kg/s)
297.7 kg/s
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