Problem $4$: $(25$ points$)$: A coal fired power plant has the efficiency of $40\%.$ From the waste heat $($other $60\%$ of the input power$)80\%$ is captured by the cooling water and the rest rejected by the smokestack. The cooling water with the flowrate of $28\frac{m^3}{s}$ is taken from a nearby river and the temperature of that increases by $10C$ in contact with the steam in power plant. The water then returns back to the river.

a$)$ Determine the input power and capacity of the power plant in MW$.$

b$)$ What would be the temperature of the river downstream the joint if the total flowrate of the river is $120\frac{m^3}{s}$ and the temperature upstream is $15C.$