How Does the Energy Density of a Lead-Acid Battery Compare to Gasoline?

[aaronb]

Homework Statement

A fully charged 15.0 kg lead-acid battery can deliver power 1450 W for 1.0 hr. (For comparison, the "heat of combustion" of gasoline is about 44 MJ/kg.)

Battery _____ MJ/kg

Homework Equations

Unit conversion problem
1W = 1 J/s

The Attempt at a Solution

(1450 J/s / 15kg) = 96.7/10^6 = 9.6 *10^-5

 

[mgb_phys]

Please don't multiple post

 

[nlightner]

MJ/kg


The potential energy in fuels, such as gasoline, is often measured in terms of its heat of combustion, which is the amount of energy released when the fuel is burned. In this case, the "heat of combustion" of gasoline is about 44 MJ/kg. This means that for every kilogram of gasoline, approximately 44 MJ of energy can be released.

In comparison, a fully charged lead-acid battery with a mass of 15.0 kg can deliver a power of 1450 W for 1.0 hour. Using the equation 1W = 1 J/s, we can convert the power to energy by multiplying it by the time, giving us 1450 J/s * 3600 s = 5,220,000 J of energy.

To determine the potential energy in the battery per kilogram, we divide the total energy by the mass, giving us 5,220,000 J / 15 kg = 348,000 J/kg. This is significantly higher than the heat of combustion of gasoline, indicating that batteries have a higher potential energy storage capacity compared to fuels like gasoline.

In conclusion, the potential energy in a fully charged 15.0 kg lead-acid battery is approximately 348,000 J/kg, which is significantly higher than the heat of combustion of gasoline. This highlights the potential of batteries as a more efficient and environmentally friendly energy source.