A well-insulated shell-and-tube heat exchanger is used to condense a stream of t

Question

A well-insulated shell-and-tube heat exchanger is used to condense a stream of toluene. 10.0 kmol/hr of toluene vapor enters the unit at 1 atm and 120 °C, where it is cooled to 65 °C. This cooling is accomplished using liquid water that enters the heat exchanger at 10 °C and leaves at 40 °C a) Find the mass flow rate of water, in kg/hr, through the heat exchanger. b) Determine whether the process is reversible. c) If the process were reversible, then the flow rate of cooling water could be reduced without changing the temperature rise (from 10 °C 40 °C). Find the reduction in water mass flow rate, expressed as a percent relative to your answer from (a).

Explanation / Answer

a) Flow rate of toluene (mt) = 10 kmol/hr = 10 kmol/hr X 92.14 kg/kmol (Molecular mass of toluene) = 921.4 kg/hr

Initial temperature of toluene, Tt1 = 120°C

Final temperature of toluene, Tt2 = 65°C

Specific heat capacity of toluene, Cpt = 1670 J/kgK

Initial temperature of water, Tw1 = 10°C

Final temperature of toluene, Tw2 = 40°C

Specific heat capacity of toluene, Cpw = 4186 J/kgK

Q=Cpm (T1 - T2)

By overall energy balance, Heat removed from toluene = heat added to water

Cpt mt (Tt1 - Tt2) = Cpw mw (Tw2 - Tw1)

1670 X 921.4 X (120 - 65) = 4186 X mw X (40 - 10)

mw = (1670 X 921.4 X 55) / (4186 X 30)

Mass flow rate of water, mw = 673.9 kg/hr

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