A single$-$effect evaporator is used to concentrate a sugar solution from $40\%$ w$/$w to $70\%$ w$/$w sugar. Saturated steam at $140C$ is used as heat source and only latent heat is drawn from the steam. The feed at a rate of $2\mathrm{.}0k\frac{g}{s}$ enters the evaporator at the boiling point in the evaporator. The pressure in the vapour space is $101\mathrm{.}3$kPa and the boiling point rise is given by$,BPR=1\mathrm{.}78x+6\mathrm{.}22x^2.$ The overall heat transfer coefficient is $2000W{m}^{-2}{K}^{-1}.$

Calculate:

The evaporate rate $(k\frac{g}{s})$

The steam flow rate required $(k\frac{g}{s})$

The heat transfer surface area $(m^2)$

The steam economy

NOTE: Report your answer up to $2$ decimal places.