OUESTION $2(20$pts$)$

The process is consisted of a constant volume electric water heater. On a particular day, as

the tank water temperature reached the $80C,$ the heater broke down and stopped supplying

heat. At this time, water was withdrawn from this $100$ liter tank at the rate of $10$ liters$/$min;

cold water at $30C$ automatically flowed into the tank at precisely the same rate. This period

went on for exactly $5$min, and the water withdrawal was stopped at the end of the period

because of the heater design, the cold water also stopped flowing in$.$

By developing appropriate model for this process, show that, it is reasonable to consider this

a first order process, and by solving the resulting differential equation model, find the final

tank water temperature at the end of this $5-$minute period. State all your assumptions.

$({}_w=1\frac{kg}{l}$iter;$c_p=1$kca$\frac{l}{k}g-C=4184(J)*k{g}^{-1}*K^{-1})$