Exploding shoes. The rain-soaked shoes of a person may explode if ground current

Question

Exploding shoes. The rain-soaked shoes of a person may explode if ground current from nearby lightning vaporizes the water. The sudden conversion of water to water vapor causes a dramatic expansion that can rip apart shoes. Water has density 1000 kg/m^3 and requires 2256 kJ/kg to toe vaporized. If horizontal current lasts 2.12 ms and encounters water with resistivity 184 ohm-m, length 14.3 cm, and vertical cross-sectional area 15.1 times 10^-5 m^2, what average current (in A) is required to vaporize the water? Number _________ Units

Explanation / Answer

volume, V = 15.1X10-5 * 0.143 = 2.1593e-5 m3

mass, m = density x volume = 1000*2.1593e-5 = 2.1593e-2 kg

heat, Q = mL = 2.1593e-2 * 2256x103 = 4.87e+4 J

Resistance, R = rho*L/A = 184*0.143 / 15.1X10-5 = 1.7425e+5 Ohm

Current: I = sqrt[Q/R*t]

                = sqrt[4.87e+4 /1.7425e+5 * 2.1e-3 ]

                = 11.48 A

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