During a particular thunderstorm, the electric potential differencebetween the c

Question

During a particular thunderstorm, the electric potential differencebetween the clouds and the ground
is Vcloud Vground = 109 Volts with the cloud being at thehigher potential. Now, there is a
lightning flash in which a charge of -25 C is transferred from theground to the cloud.

(a) How much work is done on the charge by the electric force.

(b) If the work done by the electric
force were instead used to accelerate a 1100-kg automobile fromrest, what would be its final
speed?

(c) If the work done were converted to heat, how many kiligrams ofwater at room
temperature could be vaporized. Recall, the heat energy required tovaporize a certain mass m
of water is Q = cmT + mL where the specific heat capacity of waterat room temperature is
approximately c 4186J/(kg · Co), the latent heat ofvaporization of water is L = 22.6 × 105J/kg
and the temperature change is T (100 20)Co.

Explanation / Answer

Potential difference V = 109 Volts
Charge q = -25 C (a) work is done on the charge by the electricforce W = Vq                                                                                    = 2725 J

(b) mass m = 1100-kg Initial velocity u = 0 Let the final speed be v then W = ( 1/ 2) m[ v^2 - u^2 ]            = ( 1/ 2) mv^2 from this final speed v = [2W / m]                                  = 2.225 m /s (c) let the mass of the water be m then  Q = cmT + mL Where the specific heat capacity of water at room temperatureis c = 4186J/(kg · Co) the latent heat of vaporization of water is L = 22.6× 105J/kg
the temperature change is T = (100 20)Co. = 80Co from problem Q = W plug the values weget 2725 = m [ 334880 + 22.6*10^5]                                      m = 1.05*10^-3 kg

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