The capacity of a storage battery, such those used in automobile electrical syst

Question

The capacity of a storage battery, such those used in automobile electrical systems, is rated in ampere-hours (A = h). A50 A b battery can supply a current of 50 A for 1.0 h, or 25 A for 2.0 h, and so on. What total energy can be supplied by a 10 V, 40 A b battery if its internal resistance is negligible? Express your answer using two significant figures. What volume (in titers) of gasoline has total heal of combustion equal to the energy obtained in part (a)? (See Section 17.6: the density of gasoline is 900 kg/m^3.) Express your answer using two significant figures. If a generator with an average electrical power output of 0.50 kW is connected to the battery, how much time will be required for it to charge the battery fully? Express your answer using two significant figures.

Explanation / Answer

(A) Rate of energy supplied, P = V I

total energy supplied = P t = V I t

= (10 V) (40 A ) (3600sec)

= 1.4 x 10^6 J

(B) heat of Combustion of gasoline = 47 MJ/kg

gasoline required = (1.4 MJ) / (47 MJ/kg) = 0.0306 kg

Volume = 0.0306 / 900 = 3.4 x 10^-5 m^3 = 0.03 L

(C) Q = P t

1.4 x 10^6 = (0.50 x 10^3 W)(t)

t = 2880 sec Or 0.8 hrs

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