A storm cloud and the ground represent the plates of a capacitor. During a storm

Question

A storm cloud and the ground represent the plates of a capacitor. During a storm, the capacitor has a potential difference of 2.00 times 108 V between its plates and a charge of 40.0 C. A lightning strike delivers 1.00% of the energy of the capacitor to a tree on the ground. How much sap in the tree can be boiled away? Model the sap as water initially at 26.0 degree C. Water has a specific heat of 4 186 J/kg degree C, a boiling point of 100 degree C, and a latent heat of vaporization of 2.26 times 106 J/kg.

Explanation / Answer

Start with the Energy in a capacitor

E = .5QV = (.5)(40)(2 X 10^8)

E = 4 X 10^9 J

1 percent of that is 4.0 X 10^7 J

Now Q = mc(delta T) + m(H)

4.0 X 10^7 = (m)(4186)(100 - 26) + (m)(2.26 X 10^6)

4.0 X 10^7 = 2.57 X 10^6m

m = 15.6 kg

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