A cold beverage can be kept cold even on a warm day if it is slipped into a poro

Question

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 = 17.4 degreeC, the environment has temperature T_env = 34.7 degreeC, and the container is a cylinder with radiu: r = 2.52 cm and height 10.5 cm. Approximate the emissivity as epsilon = 0.817, and neglect other energy exchanges. At what rate dm/dt is the container losing water mass

Explanation / Answer

q =(T1^4 - T2^4)*A

A = area of cylinder = 2rl

= 2*0.0252 * 0.105

So,

q = 0.817*5.6703*10^-8*((273+34.7)^4 - (273+17.4)^4) * 0.02

= 1.71 J/s

SO this is the heat supplied / sec

To calculate water mass,

1kg requies 333KJ of energy

So, dm/.dt =1.71 / 333 = 5.13 mg/s

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