A cylindrical tank of height 2 m with a crossesctional area of 0.5 m2 contains hot water at 80?C, 125 kPa. It is in a room with temperature T0 = 20?C, so it slowly loses energy to the room air proportional to the temperature difference as
with the tank surface area, A, and C is a constant. For different values of the constant C, estimate the time it takes to bring the water to 50?C. Make enough simplifying assumptions so that you can solve the problem mathematically, that is find a formula for T(t).