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A pitcher with porous walls 1 mm thick holds 10 kg of water that seeps to the outer surface and evaporates at 0.1 g/s. The outer surface area is 200 cm², the room is at 42 C, latent heat of vaporization is 2.27 x 10⁶ J/kg, and the wall thermal conductivity is 0.80 J/m-s-C. Estimate the steady-state temperature of the water inside.

1. 28 C
2. 30 C
3. 32 C
4. 34 C

Correct answer: 28 C

Solution

Conducted power = evaporation power: 0.80*0.02*(42 - T)/0.001 = 1e-4 * 2.27e6 => (42 - T) ~ 14, T ~ 28 C.

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