An electrically heated tank for hot water contains 200 kg of liquid water at 80C in order to kill Legionella. Water is provided at constant temperature of 10 C and is withdrawn from the tank at a steady rate of dm/dt= 0.2 kg/s. The heat losses from the tank to the surroundings are negligible, and for liquid water CV=CP=4.18 kJ/(kg*K), independent of T and P. Assuming negligible heat losses from the tank to the surroundings, the tank is designed in such a way that if power outage occurs, an amount of (Q/s) heat/second is automatically and uniformly provided to the tank to maintain a steady state-flow process. a) In case of a power outage, what is the rate of heat Q/s that needs to be provided to the tank to maintain a steady state-flow process? b) An error occurred in the design, and the rate of heat provided to the tank is 10 kJ/s less than the appropriate amount of heat calculated in part a, and thus the total rate Q/s provided is not sufficient to maintain a steady-state-flow process after the error occurs. How long will it take for the temperature of the output stream to reach 78C)? You can use the following integral: