Batches of caustic solution for the waste liquor neutralizer are prepared by filling the NaOH makeup tank with the required amount of mixed salt solution at 25°C, then adding the required mass of NaOH pellets, also at 25°C, and immediately starting an agitator to aid the dissolution process. When solid NaOH dissolves in water, a great deal of thermal energy is released. To keep the batch from getting too hot, cooling water initially at 15°C is pumped through the jacket surrounding the makeup tank. The dissolution is complete after four hours. The flow of coolant is continued after that point until the tank contents are brought back down to 25°C, whereupon the cooling water flow and the tank agitator are turned off and the batch is dumped to the NaOH feed drum.

An integral energy balance on the tank contents from t = 0 to an arbitrary time has the form

where

(a) Heat is transferred from the tank to the coolant at an average rate of 2.5 × 10 kJ/h during the production of a batch of solution. The agitator has a maximum power rating of 20 kW. At the agitation rate used in the mixing process, about 65% of the rated power is actually drawn, of which 80% is transferred as shaft power to the tank contents and the remaining 20% is lost as wasted heat to the surroundings. Use this information to calculate the values of (kJ/h) and Ẇ_s(kJ/h) in the given energy balance equation. (Make sure the values have the correct signs.)

(b) Calculate the temperature in the reactor at the moment the NaOH has completely dissolved (t = 4 h). Use heat of solution data from Table B.11 in your calculation and take the average heat capacity of the tank contents to be 3.8 kJ/(kg∙°C).

(c) How long must the cooling be continued after dissolution is complete to bring the solution temperature down to 25°C? (Remember that the agitator is turned off during this phase of the operation.) What is the total time required to produce a batch from the moment the sodium hydroxide pellets are added?

(d) Starting with the first law of thermodynamics for a closed system operating at constant pressure [Q(kJ) - W_s(kJ) = ΔH(kJ), where -W_s is the total shaft work added to the system], derive the given energy balance equation by defining a suitable process path for the determination of ΔH.

Transcribed Image Text:

Qt – W,t = NNAOH AĤÇ + Msoin Cp(T – 25)