Fundamentals of Food Process Engineering

Romeo T. Toledo

Chapter 5

Energy Balances - all with Video Answers

Educators

Chapter Questions

Problem 1

What would be the pressure generated when milk is heated to $135^{\circ} \mathrm{C}$ in a closed system? If the system is not pressurized, can this temperature be attained?

Rashmi Sinha

Rashmi Sinha

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Problem 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 $150^{\circ} \mathrm{F}$.

Rashmi Sinha

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Problem 3

If a retort indicates a pressure of 15 psig but mercury in glass thermometer registers only $248^{\circ} \mathrm{F}$, what does this indicate? Assume that both instruments are in working order and have been properly calibrated.

Rashmi Sinha

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Problem 4

An evaporator is operated at $15 \mathrm{in}$. $\mathrm{Hg}$ vacuum. What would be the temperature of the product inside the evaporator? Assume product has the same boiling point as water.

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Problem 5

How much heat is required to convert $1 \mathrm{~kg}$ water at $20^{\circ} \mathrm{C}$ to steam at $120^{\circ} \mathrm{C}$ ?

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Problem 6

How much heat must be removed to convert $1 \mathrm{lb}$ steam at $220^{\circ} \mathrm{F}$ to (a) water at $220^{\circ} \mathrm{F}$; (b) water at $120^{\circ} \mathrm{F}$ ?

Rashmi Sinha

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Problem 7

One pound of steam at $260^{\circ} \mathrm{F}$ 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 $200^{\circ} \mathrm{F}$ ?

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Problem 8

At what temperature would water be expected to boil at $10 \mathrm{in}$. $\mathrm{Hg}$ vacuum? Atm pressure = 14.696 psia.

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Problem 9

How much steam at $250^{\circ} \mathrm{F}$ would be required to heat $10 \mathrm{lb}$ of water from $70^{\circ} \mathrm{F}$ to $210^{\circ} \mathrm{F}$ in a direct steam injection heater?

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Problem 10

How much heat will be required to convert steam at 14.696 psig to superheated steam at $600^{\circ} \mathrm{F}$ at the same pressure?

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Problem 11

Ten pounds of water at a pressure of $20 \mathrm{psig}$ is heated to a temperature of $250^{\circ} \mathrm{F}$. 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?

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Problem 12

(a) If water at $70^{\circ} \mathrm{F}$ 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 $14.696 \mathrm{psia}$, what will be the final pressure?

Rashmi Sinha

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Problem 13

Determine the heat content in BTU/lb for water (it could be liquid, saturated steam, or superheated steam) under the following conditions: (a) $180^{\circ} \mathrm{F}$ and 14.696 psia pressure, (b) $300^{\circ} \mathrm{F}$ and $14.696 \mathrm{psia}$ pressure, (c) $212.01^{\circ} \mathrm{F}$ and $14.696 \mathrm{psia}$ pressure.

Rashmi Sinha

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Problem 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 $26.67^{\circ} \mathrm{C}\left(80^{\circ} \mathrm{F}\right)$ and this is preheated to $90.56^{\circ} \mathrm{C}\left(195^{\circ} \mathrm{F}\right)$ by direct steam injection using culinary steam (saturated) at $104.4^{\circ} \mathrm{C}\left(220^{\circ} \mathrm{F}\right)$ 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.

Rashmi Sinha

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Problem 15

A fruit juice at $190^{\circ} \mathrm{F}$ is allowed to flash into an essence recovery system maintained at a vacuum of 29 in. of mercury. Atmospheric pressure is $29.9 \mathrm{in}$. 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 $0.2 \mathrm{BTU} /\left(\mathrm{lb} \cong{ }^{\circ} \mathrm{F}\right)$.
(c) The quantity of water vaporized per $100 \mathrm{lb}$ of juice entering the system.

Rashmi Sinha

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Problem 16

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

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Problem 17

Orange juice concentrate at $45 \%$ total solids leaves the evaporator at $50^{\circ} \mathrm{C}$. 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 $-25^{\circ} \mathrm{C}$. Assume that the sugars are all hexose sugars, and that the freezing point reduction can be determined using $\Delta \mathrm{T}_{\mathrm{f}}=\mathrm{K}_{\mathrm{f}} \mathrm{m}$, where $\mathrm{K}_f=$ the cryoscopic constant $=1.86$ and $\mathrm{m}=$ the molality. Calculate:
(a) The total heat that must be removed from the concentrate in the swept surface heat exchangers per $\mathrm{kg}$ 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 $-25^{\circ} \mathrm{C}$.

Rashmi Sinha

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Problem 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. $\mathrm{Hg}$, calculate the temperature of the fluid as it leaves the column such that when flashing occurs the desired solids content will be obtained.

Rashmi Sinha

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Problem 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 non-fat, $22 \%$ fat, and $63 \%$ water are heated from $4^{\circ} \mathrm{C}$ to $135^{\circ} \mathrm{C}$, during which time condensate accumulates within the processing vessel with the meat. Saturated steam at $135^{\circ} \mathrm{C}$ is used for heating. Calculate the total amount of meat and condensate at $135^{\circ} \mathrm{C}$.
(b) The gravy mix is of equal weight as the raw meat processed and consists of $85 \%$ water and $15 \%$ solids non-fat. Calculate the temperature of the mixture after equilibration if the gravy mix is at $20^{\circ} \mathrm{C}$ when it is pumped into the processing chamber containing the meat at $135^{\circ} \mathrm{C}$.

Rashmi Sinha

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Problem 20

The chillers in a poultry processing plant cool broilers by contacting the broilers with a mixture of water and ice. Broilers enter at $38^{\circ} \mathrm{C}$ and leave the chillers at $4^{\circ} \mathrm{C}$. 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 $/ \mathrm{h}$, and the broilers average $0.98 \mathrm{~kg}$ with a composition of $17 \%$ fat, $18 \%$ solids non-fat, 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 $15^{\circ} \mathrm{C}$, and the overflow is at $1.5^{\circ} \mathrm{C}$.

Rashmi Sinha

Numerade Educator

Problem 21

Saturated steam at $280^{\circ} \mathrm{F}$ is allowed to expand to a pressure of 14.696 psia without a loss of enthalpy. Calculate: (a) the temperature, (b) the weight of high pressure steam needed to produce $100 \mathrm{~m}^3 / \mathrm{min}$ of low pressure steam at $14.696 \mathrm{psia}$ and the temperature calculated in (a).

Rashmi Sinha

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Problem 22

In one of the systems for ultra-high-temperature sterilization, milk enters a chamber maintained at $60 \mathrm{psia}$ and $800^{\circ} \mathrm{F}$ 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 $15 \mathrm{in} . \mathrm{Hg}$ vacuum, calculate:
(a) The temperature of the milk leaving the flash chamber.
(b) The total solids content. Raw milk enters the heater at $2^{\circ} \mathrm{C}$, and contains $89 \%$ water, $2 \%$ fat, and $9 \%$ solids non-fat. Given: The enthalpy of superheated steam at 60 psia and $800^{\circ} \mathrm{F}$ is $1431.3 \mathrm{BTU} / \mathrm{lb}$. Saturated steam temperature at $60 \mathrm{psia}$ is $292.7^{\circ} \mathrm{F}$. The enthapy of saturated liquid $\left(\mathrm{h}_{\mathrm{f}}\right)$ at $292.7^{\circ} \mathrm{F}$ is $260.7 \mathrm{BTU} / \mathrm{b}$.

Rashmi Sinha

Numerade Educator

Problem 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 $20^{\circ} \mathrm{C}$ to $-20^{\circ} \mathrm{C}$.

Rashmi Sinha

Numerade Educator

Problem 24

A food mix containing $80 \%$ solids non-fat 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 $135^{\circ} \mathrm{C}$ at a pressure of $600 \mathrm{kPa}$ 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 $100^{\circ} \mathrm{C}$ 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 addtion to the extruder if the solid feed originally contains $10 \%$ water and is fed at the rate of $30 \mathrm{~kg} / \mathrm{h}$.

Rashmi Sinha

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Problem 25

A food product that contains $15 \%$ solids non-fat, $2 \%$ fat, and $83 \%$ water is to be pasteurized by heating to $95^{\circ} \mathrm{C}$ by direct steam infusion using $90 \%$ quality steam at $15 \mathrm{psig}$. After heating to $95^{\circ} \mathrm{C}$, 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.

Rashmi Sinha

Numerade Educator