A pitcher having 1 -mm thick porous walls holds 10 kg of water. Water reaches the outer surface and evaporates at a rate of 0.1 g s ⁻¹ . The surface area of the pitcher (one side) is 200 cm ^2 . The room temperature is 42^ C , the latent heat of vaporization is 2.27 10^6 J kg ⁻¹ , and the thermal conductivity of the porous walls is 0.80 J s ⁻¹ m ⁻¹ ^ C ⁻¹ . Determine the temperature of the water in the pitcher once i

Step-by-step solution

In steady state, the heat required for evaporation of water is supplied by the heat conducted from the surroundings through the walls of the pitcher. The rate of heat required for evaporation is: dQ dt = L dm dt Substituting the given values: dQ dt = (2.27 10^6 J kg ⁻¹) (0.1 10⁻³ kg s ⁻¹) = 227 J s ⁻¹ The rate of heat conduction through the walls is given by: dQ dt = K A (T₀ - T) d Equating the two rates: 0.80 (200 10⁻⁴) (42 - T) 10⁻³ = 227 0.016 10⁻³ (42 - T) = 227 16(42 - T) = 227 42 - T = 227 16 = 14.1875 T = 42