$1.$Applesauce is manufactured by heating chopped apple slices $($Cp$=3670$ J$/$kg K$)$ from $20\backslash$deg Cto $100\backslash$deg C in a steam kettle with continuous agitation. The apples initially contain $89\%$moisture and after cooking contain $72\%$ moisture.a$)$What flow rate of apple slices is required to produce a sauce production rate of $50$kg$/$h$?$b$)$If saturated steam at $110\backslash$deg C is used in the kettle and condensate is removed at$105\backslash$deg C$,$ how much steam is required?c$)$The applesauce $($Cp$=3187$ J$/$kg K$)$ is cooled from $100\backslash$deg to $20\backslash$deg C in a scraped$-$ surfaceheat exchanger with an overall heat transfer coefficient of $568$ W$/$m$2$K$.$ Coolingwater enters the heat exchanger at $10\backslash$deg C$,$ flows countercurrent and exits at $17\backslash$deg C$.$Calculate the mass flow rate of cooling water required. d$)$ Calculate the heat transferarea required