Energy Balances

Abstract

“Energy” used to be a term that everybody took for granted. Now, to a layman, energy has been added to the list of the basic necessities of life. Increasing energy costs have forced people to recognize and appreciate the value of energy more than ever before. Energy conservation is being stressed not only in industrial operations but also in almost all aspects of an individual’s daily activities.

Problems

• 4.1. What would be the pressure generated when milk is heated to 135 °C in a closed system? If the system is not pressurized, can this temperature be attained?

• 4.2. A method for heating food with saturated steam at temperatures below the boiling point of water is by carrying out the process under a vacuum. At what vacuum should a system be operated to heat a material with saturated steam at 150 °F?

• 4.3. If a retort indicates a pressure of 15 psig but mercury in glass thermometer registers only 248 °F, what does this indicate? Assume that both instruments are in working order and have been properly calibrated.

• 4.4. An evaporator is operated at 15 in. Hg vacuum. What would be the temperature of the product inside the evaporator? Assume product has the same boiling point as water.

• 4.5. How much heat is required to convert 1 kg water at 20 °C to steam at 120 °C?

• 4.6. How much heat must be removed to convert 1 1b steam at 220 °F to (a) water at 220 °F and (b) water at 120 °F?

• 4.7. One pound of steam at 260 °F contains 80% steam and 20% liquid water. How much heat will be released by this steam when it is allowed to condense to water at 200 °F?

• 4.8. At what temperature would water be expected to boil at 10 in. Hg vacuum? Atm pressure = 14.696 psia.

• 4.9. How much steam at 250 °F would be required to heat 10 lb of water from 70 °F to 210 °F in a direct steam injection heater?

• 4.10. How much heat will be required to convert steam at 14.696 psig to superheated steam at 600 °F at the same pressure?

• 4.11. Ten pounds of water at a pressure of 20 psig is heated to a temperature of 250 °F. If this water is allowed to empty into an open vessel at atmospheric pressure, how much of the water will remain in the liquid phase?

• 4.12. (a) If water at 70 °F is introduced into an evacuated vessel where the original pressure is 0 psia, what would be the pressure inside the vessel at equilibrium? Assume no change in the temperature of water. (b) If the original pressure is 14.696 psia, what will be the final pressure?

• 4.13. Determine the heat content in BTU/lb for water (it could be liquid, saturated steam, or superheated steam) under the following conditions: (a) 180 °F and 14.696 psia pressure, (b) 300 °F and 14.696 psia pressure, and (c) 212.01 °F and 14.696 psia pressure.

• 4.14. In the formulation of a pudding mix, it is desired that the solids content of the product would be 20%. The product leaving the batch tank has a temperature of 26.67 °C (80 °F), and this is preheated to 90.56 °C (195 °F) by direct steam injection using culinary steam (saturated) at 104.4 °C (220 °F) followed by heating in a closed system to sterilizing temperatures. There is no further loss or gain of moisture in the rest of the process. What should be the solids content of the formulation in the batch tank such that after the direct steam injection heating the final solids content of the product will be 20%? Use Siebel’s equation for calculating the specific heat of the product.

• 4.15. A fruit juice at 190 °F is allowed to flash into an essence recovery system maintained at a vacuum of 29 in. of mercury. Atmospheric pressure is 29.9 in. The vapors that flash off are rectified to produce an essence concentrate, and the juice after being stripped of the aromatic constituents is sent to an evaporator for concentration.

  • Assuming sufficient resident time for the juice in the system to allow equilibrium in temperature between the liquid and the vapor, calculate:

    • (a) The temperature of the juice leaving the essence recovery system.

    • (b) The solids content of the juice leaving the system if the original solids content is 10%. Assume no additional heat input and the latent heat for vaporization is derived from the loss in sensible heat of the liquid. The specific heat of the solids is 0.2 BTU/(lb ≅ °F).

    • (c) The quantity of water vaporized per 100 lb of juice entering the system.

• 4.16. An evaporator has a heat transfer surface area that would allow the transfer of heat at the rate of 100,000 BTU/h. If this evaporator is concentrating apple juice from 10% to 45% solids, under a vacuum of 25 in. Hg (atmospheric pressure is 30 in. of mercury), how much apple juice can be processed per hour?

• 4.17. Orange juice concentrate at 45% total solids leaves the evaporator at 50 °C. This is frozen into slush in swept surface heat exchangers until half of the water is in the form of ice crystals prior to filling into cans, and the cans are frozen at −25 °C. Assume that the sugars are all hexose sugars and that the freezing point reduction can be determined using ΔT_f = K_fm, where K_f = the cryoscopic constant = 1.86 and m = the molality. Calculate:

  • (a) The total heat that must be removed from the concentrate in the swept surface heat exchangers per kg of concentrate processed

  • (b) The amount of heat that must be further removed from the concentrate in frozen storage

  • (c) The amount of water still in the liquid phase at −25 °C

  Note: The moisture content is beyond the range where Chang and Tao’s correlation is applicable. Determine the freezing point by calculating the freezing point depression: ΔT_b = K_fm. The specific heat of the solids is the same below and above freezing. The specific heat of ice is 2093.4 J/(kg$K). The heat of fusion of ice is 334,860 J/kg. The juice contains 42.75% soluble solids.

• 4.18. In a falling film evaporator, fluid is pumped to the top of a column and the fluid falls down as a film along the heated wall of the column increasing in temperature as it drops. When the fluid emerges from the column, it is discharged into a vacuum chamber where the fluid drops in temperature by flash evaporation until it reaches the boiling temperature at the particular vacuum employed. If juice containing 15% solids is being concentrated to 18% solids in one pass through the heated column, and the vacuum in the receiving vessel is maintained at 25 in. Hg, calculate the temperature of the fluid as it leaves the column such that when flashing occurs the desired solids content will be obtained.

• 4.19. When sterilizing foods containing particulate solids in the Jupiter system, solids are heated separately from the fluid components by tumbling the solids in a double cone processing vessel with saturated steam contacting the solids. The fluid component of the food is heated, held until sterile, and cooled using conventional fluid heating and cooling equipment. The cooled sterile liquid is pumped into the double cone processing vessel containing the hot solids, which cools the latter and drops the pressure to atmospheric. After allowing the mixture to cool by cooling the walls of the processing vessel, the sterile mixture is filled aseptically into sterile containers

  • (a) Meat and gravy sauce is being prepared. Beef cubes containing 15% solids nonfat, 22% fat, and 63% water are heated from 4 °C to 135 °C, during which time condensate accumulates within the processing vessel with the meat. Saturated steam at 135 °C is used for heating. Calculate the total amount of meat and condensate at 135 °C.

  • (b) The gravy mix is of equal weight as the raw meat processed and consists of 85% water and 15% solids nonfat. Calculate the temperature of the mixture after equilibration if the gravy mix is at 20 °C when it is pumped into the processing chamber containing the meat at 135 °C.

• 4.20. The chillers in a poultry processing plant cool broilers by contacting the broilers with a mixture of water and ice. Broilers enter at 38 °C and leave the chillers at 4 °C. USDA requires an overflow of 0.5 gallons of water per broiler processed, and this must be replaced with fresh water to maintain the liquid level in the chiller. Melted ice is part of this overflow requirement. If a plant processes 7000 broilers/h and the broilers average 0.98 kg with a composition of 17% fat, 18% solids nonfat, and 65% water, calculate the ratio by weight of ice to fresh water that must be added into the chiller to meet the overflow requirement and the cooling load. Fresh water is at 15 °C, and the overflow is at 1.5 °C.

• 4.21. Saturated steam at 280 °F is allowed to expand to a pressure of 14.696 psia without a loss of enthalpy. Calculate (a) the temperature and (b) the weight of high-pressure steam needed to produce 100 m³/min of low-pressure steam at 14.696 psia and the temperature calculated in (a).

• 4.22. In one of the systems for ultrahigh-temperature sterilization, milk enters a chamber maintained at 60 psia and 800 °F in an atmosphere of superheated steam where it discharges from a plenum into vertical tubes where it falls down in a thin film while exposed to the steam. The milk will be at the boiling temperature at 60 psia on reaching the bottom of the heating chamber. After a sterilizing hold time at constant temperature, the milk is discharged into a vacuum chamber for rapid cooling. If the vacuum chamber is at 15 in. Hg vacuum, calculate:

  • (a) The temperature of the milk leaving the flash chamber.

  • (b) The total solids content. Raw milk enters the heater at 2 °C and contains 89% water, 2% fat, and 9% solids nonfat. Given: the enthalpy of superheated steam at 60 psia and 800 °F is 1431.3 BTU/lb. Saturated steam temperature at 60 psia is 292.7 °F. The enthalpy of saturated liquid (h_f) at 292.7 °F is 260.7 BTU/lb.

• 4.23. (a) Calculate the freezing point of fresh strawberries that contain 8.5% soluble solids, 1% insoluble solids, and 90.5% water. Assume that the average molecular weight of the soluble solids is 261.

• (b) If sucrose is added to the above strawberries in the ratio 1 part of sugar to 3 parts strawberries by weight, calculate the new freezing point.

• (c) Calculate the change in enthalpy of the sugared strawberries from 20 °C to −20 °C.

• 4.24. A food mix containing 80% solids nonfat and 20% fat on a dry basis is to be extruded. Water is added continuously along with the product into the extruder, and the mixture temperature increases to 135 °C at a pressure of 600 kPa at the die entrance. Extrudate leaves the die and immediately expands to atmospheric pressure, releasing vapor as it exits the die. Assume that the temperature of the extrudate is 100 °C immediately after leaving the die. It is desired that the moisture content of the extrudate will be 18% after the pressure reduction. Calculate the rate of moisture addition to the extruder if the solid feed originally contains 10% water and is fed at the rate of 30 kg/h.

• 4.25. A food product that contains 15% solids nonfat, 2% fat, and 83% water is to be pasteurized by heating to 95 °C by direct steam infusion using 90% quality steam at 15 psig. After heating to 95 °C, the product is held in a holding tube and cooled in a heat exchanger; therefore, there is no opportunity for removing added water from the steam condensate later in the process. Calculate the moisture content of the raw product entering the heater such that the desired moisture content will be obtained after heating and cooling.