A swimming pool has a surface area of 50 m and volume of 100 m. The water in the swimming pool is initially at 15C. A heater is being designed to maintain a steady-state pool temperature of 25C. The heat loss occurs mainly on the surface of the pool and can be calculated as a heat flux as follows: Jy=kn (Twater - Tair, wet bulb) where J, is the heat flux (J/m s or W/m), kn is the heat trnsfer coefficient (50 W/mK), Twater is the temperature of the water, and Tair, wet bulb is the wet bulb temperature of the air and can be assumed constant at 15C. Assume that water has a density of 1000 kg/m and a heat capacity of 4184 J/kg K. a. Carry out a heat balance at steady state to calculate the heater power needed. (10 points) b. Use a nonsteady-state equation to derive an equation for the temperature of the pool as a function of time once the heater is started. The resulting equation should be in the form of T = f(t). (10 points) c. Calculate the time needed to reach water temperature of 24C. (5 points)