Q$3.$ A fruit juice is going to be concentrated in a two$-$stage evaporator. We have $10k\frac{g}{s}$ of a juice composed by $92\%$ water, $7\mathrm{.}5\%$ soluble solids and $0\mathrm{.}5\%$ insoluble solids $($in suspension$).$ At the end of the process, the water content should be only $60\%.$

a$)$ Perform the overall mass balance and determine the composition of the concentrate and the quantity of water that needs to be evaporated

b$)$ Perform the energy balance and determine the amount of energy that needs to be supplied if all this would be done in one evaporator working at a temperature of $65C($and corresponding vacuum for boiling at this temperature$)$

c$)$ If all this energy would be supplied by saturated steam at $1$ bar and $100C($leaving the evaporator as liquid water at the boiling point$),$ what is the flow rate of steam that is needed?

The latent heat of evaporation of water at the following temperatures $($and corresponding vapour pressures$)$ is: $65C$:$2355k\frac{J}{k}g,70C$:$2336k\frac{J}{k}g,100C$:$2256k\frac{J}{k}g$

Assume that the specific heat of fruit juice, regardless of its concentrotion, is $.($:$C$