Question

A water drop slung onto a skillet with a temperature between 100°C and 200°C will remain...

A water drop slung onto a skillet with a temperature between 100°C and 200°C will remain a liquid for about 1 second. However, if the skillet is much hotter the drop can last several minutes. This is due to the Leidenfrost Effect, named after an early investigator (circa 1756). 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 distance L, as shown in the figure).

Let L = 0.100 mm. Assume that the drop is flat with a height h = 1.50 mm and that the surface area of the bottom face is 4.00 x 10-6 m2. Also, assume that the skillet is at a constant temperature of 300 °C and that the drop has a temperature of 90 °C. Water has a density of 1000 kg/m3, the supporting layer of air & vapor has a thermal conductivity of 0.026 W/m∙K, the specific heat of water is 4190 J/ kg∙K, and the Latent heat of vaporization for water is 2256 x 103J/kg. We will assume that thermal energy is only being transported via conduction.

a. What is the heat transfer rate between the skillet and the drop?

b. How much thermal energy is needs to be added to the water drop to convert it to steam at 100°C?

(Recall that the volume of a right circular cylinder is the area of its base multiplied by its height).

c. How long does it take for the entire drop to be converted into steam?

d. Which of our assumptions may not fit very well with what is actually happening? Explain your reasoning.

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