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Sagot :
The mass of sap in the tree is 96.2 kg
Electrical energy between the cloud and ground
The electrical energy between the cloud and ground is the energy stored in a capacitor W = 1/2QV where
- Q = charge between cloud and ground = 50.0 C and
- V = potential difference between cloud and ground = 1.00 × 10⁸ V.
So, W = 1/2QV
= 1/2 × 50.0 C × 1.00 × 10⁸ V
= 25.0 × 10⁸ J
Energy used to boil sap
The energy used to boil the sap from 30 °C to 100 °C and modelling the sap as water, is
E = mc(T' - T) + mL where
- m = mass of sap,
- c = specific heat capacity of sap = 4200 J/kg-°C,
- T = initial temperature of sap = 30 °C,
- T' = final temperature of sap = 100 °C and
- L = latent heat of vaporization of sap = 226,000 J/kg
Mass of sap
Making m subject of the formula, we have
m = E/[c(T' - T) + L]
Now since energy the lightning bolt delivers to the sap is 2.00 %. So, E = 2.00 % W, we have that E = 0.02W
So, m = 0.02W/[c(T' - T) + L]
Substituting the values of the variables into the equation, we have
m = 0.02W/[c(T' - T) + L]
m = 0.02 × 25.0 × 10⁸ J/[4200 J/kg-°C(100 °C - 30 °C) + 226,000 J/kg]
m = 0.5.0 × 10⁸ J/[4200 J/kg-°C(70°C) + 226,000 J/kg]
m = 0.5 × 10⁸ J/[294000 J/kg + 226,000 J/kg]
m = 5 × 10⁷ J/520000 J/kg
m = 50 × 10⁶ J/0.52 × 10⁶ J/kg
m = 96.15 kg
m ≅ 96.2 kg
The mass of sap in the tree is 96.2 kg
Learn more about heat energy here:
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