A water drop will last about 1 [sec] on a hot skillet with a temperature between

Question

A water drop will last about 1 [sec] on a hot skillet with a temperature between T = 100 [C] and about 200 [C]. However, if the skillet is much hotter, the drop can last several minutes, an effect named after an early investigator. The longer lifetime is due to the support of a thin layer of air and water vapor that separates the drop from the metal by a thin layer of gas. Assume that the skillet is at temperature T = 250 [C]. Also, assume that the drop is flat with height h = 1.60 [mm] and bottom face area A = 4 [mm2 ] and with a thin gas layer underneath of thickness s = 0.100 [mm]. a) If the thermal conductivity of the gas layer is k = 0.026 [W/m/K], at what rate is heat energy conducted across from the skillet to the water drop. b) If heat conduction is the primary way energy is transferred from the skillet to the droplet and if the drop evaporates by maintaining the ratio of thickness and diameter, how long will the drop last? Note that the area of the drop is decreasing with time. The latent heat of vaporization is Lv = 2.256×106 [J/kg].

Explanation / Answer

the rate of energy flow through the surface

P = kA(Ts - Tw)/L

k = 0.026 W/m/K

A = 4*10^-6

Ts - Tw = 250 - 100 = 150

L = 1.6*10^-3

SO,

P = 0.026*4*10^-6*150/0.0001 = 0.156 W

B.

P*t = Lv*m

m = rho*V = rho*A*h

t = Lv*rho*A*h/P

t = 2.256*10^6*1000*4*10^-6*1.6*10^-3/0.156

t = 92.55 sec

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