During a lightning flash, there exists a potentialdifference of V cloud - V grou

Question

During a lightning flash, there exists a potentialdifference of Vcloud -Vground = 1.2 × 109 V betweena cloud and the ground. As a result, a charge of -25 C istransferred from the ground to the cloud.

(a)  

How much work Wground–cloud is done onthe charge by the electric force?

(b)  

If the work done by the electric force were used to accelerate a1100-kg automobile from rest, what would be its final speed?

(c)  

If the work done by the electric force were converted into heat,how many kilograms of water at 0 °C could be heated to 100°C?

(a)  

How much work Wground–cloud is done onthe charge by the electric force?

(b)  

If the work done by the electric force were used to accelerate a1100-kg automobile from rest, what would be its final speed?

(c)  

If the work done by the electric force were converted into heat,how many kilograms of water at 0 °C could be heated to 100°C?

Explanation / Answer

(a) The amount of work Wground-cloud is done on thecharghe by the electric force is                   Wground-cloud = Vq                                         = (1.2*109V)(25C)                                         = 30.0*109J (b) Initial speed (u) of the automobile = 0 Let v be the final speed of the automobile. Mass (m) of the automobile = 1100 kg Then according to the work-energy theorem, the workdone by theautomobile is equal to the change in its kinetic energy. so W = KEfinal - KEinitial           =(1/2)mv2 - (1/2)mu2          =(1/2)mv2 - 0          =(1/2)mv2       v = (2W / m) Here W = 30.0*109J          m = 1100kg (c) Specific heat of water is c = 4186 J/kg.Co Temperature difference is T = 100oC We know that Q = mcT                       m = Q / (cT) Here Q = 30.0*109J          =(1/2)mv2 - 0          =(1/2)mv2       v = (2W / m) Here W = 30.0*109J          m = 1100kg (c) Specific heat of water is c = 4186 J/kg.Co Temperature difference is T = 100oC We know that Q = mcT                       m = Q / (cT) Here Q = 30.0*109J

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