posted by Anonymous .
An electric car uses a lithium metal hydride battery with a mass of 250 kg. The battery delivers 300v and holds a stored charge q of 70 ampere-hours.
Calculate the total energy stored in the battery in kWh. Calculate the number of gallons of gas that would have an equivalent stored energy
300 x 70 = 21,000 Watt-hours = 2.1 kWh is the stored battery energy
Gasoline contains 45.8 MJ/kg of chemical energy, but only about 1/3 of that is available as work, due to the second law of thermodynamics.
1 kW*h = 3600 *1000 = 3.6*10^6 Watt-seconds (Joules), so the 2.1 kWh in the battery is equivalent to 7.56*10^6 J = 7.56 MegaJoules
To get that much energy from gasoline, at 1/3 efficiency, you would need about 1/2 kg, which would be about 1/8 gallon.