Walker, Halliday & Resnick — Temperature, Heat, and the First Law of Thermodynamics: Problem 22

22 Evaporative cooling of beverages. A cold beverage can be kept cold even on a warm day if it is slipped into a porous ceramic container that has been soaked in water. Assume that energy lost to evaporation matches the net energy gained via the radiation exchange through the top and side surfaces. The container and beverage have temperature \( T = 10^\circ\text{C} \), the environment has temperature \( T_{\text{env}} = 32^\circ\text{C} \), and the container is a cylinder with radius \( r = 2.2 \text{ cm} \) and height \( 10 \text{ cm} \). Approximate the emissivity as \( \varepsilon = 1 \), and neglect other energy exchanges. At what rate \( dm/dt \) is the container losing water mass?