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

Question

48 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 be vaporized. If horizontal current lasts 2.00 ms and encounters water with resistivity 150 omega, length 12.0 cm, and vertical cross-sectional area 15 X10 m^2, what average current is required to vaporize the water?

Explanation / Answer

Note that

R = (rho)L/A

where

R = resistance
rho = resistivity (150 ohm*m)
L = length (12.0 cm = 0.120 m)
A = cross sectional area (15E-5 m^2)

Thus,

R = 120 000 ohms

Note that

Work done by lightning = I^2 R t

where

I = current
R = resistance
t = time (2.00 ms = 2E-3 s)

Also, note that

Work to vaporize = LDAl

where L = latent heat of vaporization (2256000 J/kg)
D = density (1000 kg/m^3)

Thus,

Work done by lightning = Work to vaporize

I^2 R t = LDAl

Isolating I,

I = sqrt(LDAl/Rt)

Thus,

I = 13.01 A [ANSWER]

DONE! It was nice working with you!

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