Question

While you are studying for an upcoming physics exam, a lightning storm is brewing outside your window. Suddenly, you see a tree across the street struck by lightning. There is a loud sound and you see smoke rising from various parts of the tree. You stop studying for your exam and do online research on lightning, trees, and sap. You find that a typical lightning bolt represents a potential difference of 1.00 ✕ 108 V between the cloud and the ground and that it can transfer a typical charge of 50.0 C between the cloud and the ground. Some models show that when a tree is hit by lightning, perhaps 2.00% of the energy in the lightning bolt can be delivered to the sap, causing it to boil. Model the sap as water initially at 30.0°C. If all of the sap in the tree is vaporized to gaseous sap at 100°C, determine how much sap (in kg) there is in the tree. (Use any necessary values found in this table or this table.)

Answer 1

The information given regarding the lightning illustrates that the amount of sap in the tree is 39.63kg.

How to calculate the amount of sap

From the information given,

∆V = 1 × 10⁸

Q = 50°C

The energy carried by the change will be:

= Q∆V

= 1 × 10⁸ × 50

= 50 × 10⁸ J

The 2% of the energy will be:

= 2% × 50 × 10⁸ J

= 1 × 10⁸ J

Latent heat of boiling = 2230000J

Specific heat = 4.186J/k

Q1 = 4186 × (100 - 30)

= 4186 × 70

= 239020 J/kg

Q2 = 2230000 J/kg

U = Q1 + Q2

1 × 10⁸ = 239020 + 2230000.

m = (1 × 10⁸) / (239020 + 2230000)

m = 39.63kg

In conclusion, the correct option is 39.63kg.

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