Suppose that a storm cloud has a potential difference of30*10 6 V relative to a

Question

Suppose that a storm cloud has a potential difference of30*106 V relative to a tree. a. If during a lightning strike, 50 C of charge is transferredthrough this potential difference, determine how much energy istransferred from the cloud to the tree. b. Suppose that 2.4% of the energy computed in part (a) isabsorbed by the tree, determine how much water (sap in the tree)can be boiled away, starting at 30oC. Assume thatwater has a specific heat of c = 4186 J/(kg * oC), aboiling point of 100oC, and a heat of vaporization of h= 2.26*106 J/kg. Note that c is the energy neededto heat one kilogram of water by 1oC, and h is theenergy needed to boil one kilogram of water. Suppose that a storm cloud has a potential difference of30*106 V relative to a tree. a. If during a lightning strike, 50 C of charge is transferredthrough this potential difference, determine how much energy istransferred from the cloud to the tree. b. Suppose that 2.4% of the energy computed in part (a) isabsorbed by the tree, determine how much water (sap in the tree)can be boiled away, starting at 30oC. Assume thatwater has a specific heat of c = 4186 J/(kg * oC), aboiling point of 100oC, and a heat of vaporization of h= 2.26*106 J/kg. Note that c is the energy neededto heat one kilogram of water by 1oC, and h is theenergy needed to boil one kilogram of water.

Explanation / Answer

they want you to treat the situation as a capacitor, so .    energy stored in a cap = (1/2) Q V =(1/2) * 50 *30 x 106   = 750 x106 Joules . The question is poorly worded, and they give you theimpression that energy = QV    but when Iassigned this problem for my students, we found that webassignwants    energy = (1/2) QV . Anyway...   2.4% of this is absorbed by the tree,so .           energy absorbed = 0.024 * 750 x 106  =   18 x 106   Joules . energy to boil water = mcT + mL     so .,               18x 106   =    m * 4186 *70 + m * 2260000 .           18 x 106 = m ( 0.293020   + 2.26 ) x 106 .    m =    7.05 kg   is boiledaway         (if you usedenergy = QV you would get twice this amount   14.1kg) .    m =    7.05 kg   is boiledaway         (if you usedenergy = QV you would get twice this amount   14.1kg)

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