A couple of BSE students designed a small-scale continuous juice pasteurizer As

Question

A couple of BSE students designed a small-scale continuous juice pasteurizer As illustrated below, the pasteurizer features a tube-in-tube exchanger which uses incoming (i.e. cold) |juice to cool down the juice that has been pasteurized Juice that has been pasteurized (i.e. that exiting the holding tube) wans up the incoming juice on its way out through the tube-in-tube exchanger Juice is pumped through the system at a constant rate of 4.00 Ibm/min and has a specific heat of 0.800 Btu/(lbm F). The heating element inputs energy at a rate of 1750.0 J/s. What is the difference in enthalpy of the input and output juice in Btu/min? Note that the incoming and exiting juice temperatures are given on the diagram. What is the difference in enthalpy of the input and output juice in watts? What percentage of the energy supplied by the electrical resistance heating element is lost to the environment? In other words, what percentage of the energy supplied by the element is not used to change the enthalpy of the juice? At 170 F, the hot water bath consists of 4.56 gallons of water. This must be heated from 60.0 F up to 170.0 F before juice can be pasteurized. How much energy (in Btu) does it take just to heat up this water? Assume the specific heat of water is 1.00 Btu/(lbm F). How long (in minutes) does it take the heating element to heat the water bath from 60 0 F to 170.0 F? Note that this time would not include the additional time the heating element must be on to heat the rest of the system up to 170.0F or account for heat loss to the environment. PLEASE write out problem in separate sheet and attach or use EES and print out.

Explanation / Answer

D)

total ENERGY = Mass(in lb) * specific heat capacity * temperature change

= 4.56 * 8.35 * 1 * ( 170 - 60) = 4188.36 Btu = 4.42 * 106 J

(1 Btu = 1055.06 J )

E) total time for heating = total ENERGY required / total input per sec = 4.42 * 106 / 1750 = 42 mins

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