A cylindrical tank of height 2 m with a cross sectional 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 Q_loss=C_A(T − T₀) 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).