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/m3 and requires 2256 kJ/kg to be vaporized. If horizontal current lasts 2.09 ms and encounters water with resistivity 172 Ω·m, length 15.2 cm, and vertical cross-sectional area 16.7 × 10-5 m2, what average current is required to vaporize the water?

Answer 1

I=0.41A

Step-by-step explanation:

Given,

Density:

`\rho_w = 1000Kg/m^3`

Heat vaporization

`H_v=2256kJ/Kg=2256*10^3J/Kg`

`A=16.7*10^(-5)m^2`

`L=15.2cm`

`\rho=172 \Omega`

`t=2.09ms`

Then we can calculate the mass

`m=\rho_w*A*L = (1000)(16.7*10^(-5))(0.152)= 0.02538Kg`

We know that,

Heat vaporization,
`H_v = (\upsilon)/(m)`

`\upsilon=Hv*m`

`\upsilon = 57257.28J`

Rate of energy transference,

`(1) P=(\upsilon)/(t)`

`(2) P=I*v=I^2*R`

Where
`R= \rho(L)/(A)`

Note that
`\rho=R*(A/L)`

So,

`I^2*\rho (L)/(A) = (H_v\rho_w A L )/(t)`

`I=\sqrt{(A^2H_v \rho_w)/(\rho t)}`

`I= \frac{\sqrt{(16.7*10^(-5))^2(2256*10^3)(1000)}}{(172)(2.09)}`

`I=0.41A`