Example $5\mathrm{.}5$ Cooling in downstream processing

In downstream processing of gluconic acid, concentrated fermentation broth containing $20\%(\frac{w}{w})$ gluconic acid is cooled in a

heat exchanger prior to crystallisation. $2000kg{h}^{-1}$ liquid leaving an evaporator at $90C$ must be cooled to $6C.$ Cooling is achieved

by heat exchange with $2700kg{h}^{-1}$ water initially at $2C.$ If the final temperature of the cooling water is $50C,$ what is the rate of

heat loss from the gluconic acid solution to the surroundings? Assume the heat capacity of gluconic acid is $0\mathrm{.}35cal{g}^{-1}{C}^{-1}.$