A liquid food with 12% total solids is being heated by steam injection using steam at a pressure of 232.1 kPa (Fig. E3.3). The product enters the heating system at 508C at a rate of 100 kg/min and is being heated to 1208C. The product specific heat is a function of composition as follows: cp 5 cpwðmass fraction H2OÞ 1 cpsðmass fraction solidÞ and the specific heat of product at 12% total solids is 3.936 kJ/(kg 8C). Determine the quantity and minimum quality of steam to ensure that the product leaving the heating system has 10% total solids.

Explanation:

A liquid food with 12% total solids is being heated by steam injection using steam at a pressure of 232.1 kPa (Fig. E3.3). The product enters the heating system at 50°C at a rate of 100 kg/min and is being heated to 120°C. The product specific heat is a function of composition as follows:

and the

specific heat of product at 12% total solids is 3.936 kJ/(kg°C). Determine the quantity and minimum quality of steam to ensure that the product leaving the heating system has 10% total solids.

Given

Product total solids in () = 0.12

Product mass flow rate () = 100 kg/min

Product total solids out () = 0.1

Product temperature in () = 50°C

Product temperature out () = 120°C

Steam pressure = 232.1 kPa at () = 125°C

Product specific heat in () = 3.936 kJ/(kg°C)

The mass equation is:

Also

Therefore:

The energy balance equation is:

 kJ/(kg°C)

Substituting values in the energy equation:

From properties of saturated steam at 232.1 kPa,

= 524.99 kJ/kg

= 2713.5 kJ/kg

% quality =

Any steam quality above 63.5% will result in higher total solids in

heated product

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