CHAPTER
2
MATERIAL AND ENERGY BALANCES (cont'd) SUMMARY 1. Material and energy balances can be worked out quantitatively knowing the amounts of materials entering into a process, and the nature of the process. 2. Material and energy balances take the basic form 3. In continuous processes, a time balance must be established. 4. Energy includes heat energy (enthalpy), potential energy (energy
of pressure or position), kinetic energy, work energy, chemical energy.
5. Enthalpy balances, considering only heat, are useful in many food processing situations. 
PROBLEMS 1.
If 5 kg of sucrose are dissolved in 20 kg of water estimate the concentration
of the solution in (a) w/w, (b) w/v, (c) mole fraction, (d) molar concentration.
(a) 20%, (b) 21.4% (c) 0.018 (d) 0.63 mol m^{3} 2. If 1 m^{3} of air at a pressure of 1 atm is mixed with 0.1 m^{3} of carbon dioxide at 1.5 atm and the mixture is compressed so that its total volume is 1 m^{3}, estimate the concentration of the carbon dioxide in the mixture in (a) w/w, (b) w/v, (c) mole fraction at a temperature of 25°C. Mean molecular weight of air is 28.8, and of carbon dioxide 44. (a) 18.6%, (b) 27%, (c) 0.13 3. It is convenient to add salt to butter, produced in a continuous buttermaking machine, by adding a slurry of salt with water containing 60% of salt and 40% of water by weight. If the final composition of the butter is to be 15.8% moisture and 1.4% salt, estimate the original moisture content of the butter prior to salting.(15.2%) 4. In a flour mill, wheat is to be adjusted to a moisture content of 15% on a dry basis. If the whole grain received at the mill is found to contain 11.4% of water initially, how much water must the miller add per 100 kg of input grain as received, to produce the desired moisture content? (1.8 kg/ 100 kg) 5.
(a) In an analysis, sugar beet is found to contain 75% of water and 17.5%
of sugar. Of the remaining material, 25% is soluble and 75% insoluble,
calculate the sugar content of the expressible juice assumed to contain
water and all soluble solids pro rata. 6.
A sweet whey, following cheesemaking, has the following composition: 5.5%
lactose, 0.8% protein. 0.5% ash. The equilibrium solubility of lactose
in water is:
Calculate
the percentage yield of lactose when 1000 kg of whey is concentrated in
a vacuum evaporator at 60°C to 60% solids and the concentrate is then
cooled with crystallization of the lactose, down to 20°C over a period
of weeks. 7.
In an ultrafiltration plant, whey is to be concentrated. Two streams are
to be produced, a protein rich stream and a liquid (mainly water) stream.In
all 140,000 kg per day are to be processed to provide a 12fold concentration
of 95% of the protein from an original whey concentration of 0.93% protein
and 6% of other soluble solids. 8.
It is desired to prepare a sweetened concentrated orange juice. The initial
pressed juice contains 5 % of total solids and it is desired to lift this
to 10% of total solids by evaporation and then to add sugar to give 2%
of added sugar in the concentrated juice. Calculate the quantity of water
which must be removed, and of sugar which must be added with respect to
each 1000 kg of pressed juice. 9.
A tomatojuice evaporator takes in juice at the rate of 1200 kg h^{1}.
If the concentrated juice contains 35% of solids and the hourly rate of
removal of water is 960 kg, calculate the moisture content of the original
juice and the quantity of steam needed per hour for heating if the evaporator
works at a pressure of 10 kPa and the heat available from the steam is
2200 kJ kg^{1}. Assume no heat losses. 10. Processing
water is to be heated in a direct fired heater, which burns natural
gas with a calorific value of 20.2 MJ m^{3}. If 5000 kg h^{1}
of this water has to be heated from 15°C to 80°C and the heater
is estimated to be 45% efficient, estimate the hourly consumption of
gas.
11. In a casein factory (see Fig. 2.3) the entering coagulum containing casein and lactose is passed through two cookers and acidified to precipitate the casein. The casein separates as a curd. The curd is removed pressed from the whey by screening, and then washed, and dried. The casein fines are removed from the raw whey from screening and the wash water by hydrocyclones, and mixed with the heated coagulum just before screening. The cycloned whey is used for heating in the first cooker and steam in the second cooker by indirect heating. The casein and lactose contents of the various streams were determined.
From these data calculate complete mass balances for the process, using a simple stepbystep approach, starting with the hydrocyclones. Assume lactose completely soluble in all solutions. and concentrations in fines and wastes streams from hydrocyclones are the same. (a)
Set out an overall mass balance for the complete process to the
production of the wet curd. i.e. until. after the washing/pressing operation.
Start the mass balance at the hydrocyclones i.e. mass balances for the
following unit operations: hydrocyclones, cooking, screening,washing;
and then an overall balance. Back to the top 
