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.

(See http://physics.info/energy-chemical/)

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.

To calculate the total energy stored in the battery in kilowatt-hours (kWh), we can use the formula:

Energy (kWh) = (q * V) / 1000

Where:
q = Charge in ampere-hours (Ah)
V = Voltage in volts (V)

Given:
q = 70 ampere-hours
V = 300 volts

Plugging the values into the formula:

Energy (kWh) = (70 Ah * 300 V) / 1000
Energy (kWh) = 21000 Wh / 1000
Energy (kWh) = 21 kWh

Therefore, the total energy stored in the battery is 21 kilowatt-hours.

To calculate the number of gallons of gas that would have an equivalent stored energy, we need a conversion factor. One gallon of gasoline contains approximately 33.7 kilowatt-hours of energy.

Number of gallons of gas = Energy (kWh) / Energy content of a gallon of gas (kWh/gal)

Given:
Energy content of a gallon of gas = 33.7 kWh/gal

Plugging the values into the formula:

Number of gallons of gas = 21 kWh / 33.7 kWh/gal
Number of gallons of gas = 0.624 gallons

Therefore, the amount of stored energy in the lithium metal hydride battery is equivalent to approximately 0.624 gallons of gasoline.