$[7$ points$]$ A $3$ GW nuclear power $($electrical output $=3GW)$ releases heat during power

generation and $70\%$ of the energy content of fuel is released as heat. The heat is removed

by cooling water from a nearby river. Nuclear power plants do not have stack losses. The

upstream flow is $15O\frac{m^3}{s}$ with temperature at $20C.$ Density of water $=1000k\frac{g}{m^3}$

a$.[5$ points$]$ If we want to limit the temperature rise in cooling water to $10C,$ what

should be the mass flow rate $m^{}(k\frac{g}{s})$ into and out of the power plant?

Draw a diagram showing the power plant, energy flow and the water flow. Show

the information given to you by the question on the diagram. $($Diagram $3$ pts$,$

calculation $2$ pts$)$

b$.[2$ points$]$ If we extract all the water from the river and use it to cool down the

power plant, what is the expected temperature rise $T$ in the river?