Evaporation and Concentration Questions and Answers

Answer: B

The sugar ratio is 61.54%.

The sugar ratio of sweetened condensed milk is the sugar as a percentage of the sugar solution, that is sugar plus water, because it is the concentration of sugar in the water phase that preserves the product by raising osmotic pressure:

\[ \text{Sugar ratio} = \frac{40}{40 + 25} \times 100 = 61.54\% \]

A sugar ratio around 62 to 64 percent is the standard target. 48.19, 54.16 and 56.14 do not follow from this definition.

Answer: D

Each tube must be about 3.17 m high.

Solids balance: the feed carries 150 kg/h of solids, so the 20% concentrate is 750 kg/h and 250 kg/h of water is evaporated. The heat load and the overall coefficient through the two films and the tube wall are:

\[ \begin{aligned} q &= \frac{250 \times 2309}{3600} = 160.3\ \text{kW} \\ \frac{1}{U} &= \frac{1}{5000} + \frac{0.0015}{15} + \frac{1}{800} \\ U &= 645.2\ \text{W m}^{-2}\text{K}^{-1} \end{aligned} \]

\[ \begin{aligned} A &= \frac{q}{U\,\Delta T} = \frac{160347}{645.2 \times 10} = 24.85\ \text{m}^{2} \\ H &= \frac{24.85}{100\,\pi(0.025)} = 3.16\ \text{m} \end{aligned} \]

The key takes the 10 °C as the overall temperature difference driving heat through the films and wall. The shorter tubes would supply too little area for 250 kg/h of evaporation.

Answer: A

The heat required is about 165.96 MJ.h⁻¹.

The solids are concentrated 2.7 times, so the product mass is the feed divided by 2.7, and the rest is evaporated:

\[ \begin{aligned} m_{p} &= \frac{100}{2.7} = 37.04\ \text{kg/h} \\ m_{v} &= 100 - 37.04 = 62.96\ \text{kg/h} \end{aligned} \]

Heat is needed to warm the whole feed from 30 °C to the boiling temperature of 60 °C, and then to evaporate the water:

\[ \begin{aligned} Q_{s} &= 100(3.9)(60 - 30) = 11\,700\ \text{kJ/h} \\ Q_{L} &= 62.96(2450) = 154\,259\ \text{kJ/h} \\ Q &= 165\,959\ \text{kJ/h} \approx 165.96\ \text{MJ/h} \end{aligned} \]

154.26 MJ/h is the latent heat alone, leaving out the sensible heating of the feed. 117.06 and 142.56 do not fit the mass balance: the feed must lose about 63 kg of water per hour, and that alone needs over 154 MJ.

Answer: C

The implications are R & P: a decrease in the rate of evaporation and an effect on product quality.

The vacuum pump keeps the evaporator at low pressure, so the juice boils at a low temperature. When it stops, non-condensable gases accumulate and the pressure rises, and the boiling point rises with it. The temperature difference between the heating steam and the boiling juice shrinks, so the heat transfer rate and the rate of evaporation fall (R). The juice is also held at a higher temperature, which degrades heat-sensitive flavour, colour and nutrients, for example through browning (P).

The heat needed per kilogram of water evaporated is essentially the latent heat, which changes little with the boiling temperature (it is slightly smaller at higher temperature), so there is no substantial increase in thermal energy requirement (Q).

Answer: D

The water removed is 80 kg.

The solids are not evaporated, so they balance across the concentrator:

\[ \begin{aligned} \text{solids} &= 0.05 \times 100 = 5\ \text{kg} \\ \text{concentrate} &= \frac{5}{0.25} = 20\ \text{kg} \\ \text{water removed} &= 100 - 20 = 80\ \text{kg} \end{aligned} \]

The concentrate weighs only 20 kg, so 80 kg of the original 100 kg must have gone as water. Removing 65, 70 or 75 kg would leave 35, 30 or 25 kg holding 5 kg of solids, which is 14%, 17% or 20% solids, not the required 25%.

Answer: B

The sugar ratio is 61.54%.

The sugar ratio of sweetened condensed milk is the sugar concentration in its water phase, which is what makes the product keep:

\[ \begin{aligned} \text{sugar ratio} &= \frac{\text{sugar}}{\text{sugar} + \text{water}} \times 100 \\ &= \frac{40}{40 + 25} \times 100 = 61.54\% \end{aligned} \]

The 18% total solids of the raw milk and the 1000 kg batch size are not needed for this ratio; they matter only for working out how much milk and sugar to use. The other options do not follow from the 40% sugar and 25% water.