Consider a water$-$to$-$water counter$-$flow heat exchanger with these specifications. Hot water enters at $85$oC while cold water enters at $25$oC$.$ The exit temperature of hot water is $20$oC greater than that of cold water, and the mass flow rate of hot water is $50$ percent greater than that of cold water. The product of heat transfer surface area and the overall heat transfer coefficient is $1400$ W$/$m$2$ oC$.$ Taking the specific heat of both cold and hot water to be Cp $=4180$ J$/$kg$$oC$,$ determine $($a$)$ the outlet temperature of the cold water, $($b$)$ the effectiveness of the heat exchanger, $($c$)$ the mass flow rate of the cold water $($d$)$ the heat transfer rate.