Total Battery Mass for Equal Efficiency

[PlatoDescartes]

Homework Statement

[/B]
A 12 Volt lead-acid car battery, engineered for "up to 500 or more charge/discharge cycles," has a rating of 330.0 Ampere-hours. It sells for $ 262.00.
Part B: The battery has a mass of 32.7 kg. What total mass of such batteries would be required to deliver the same effective mechanical energy as 16.0 gallons of gasoline? Assume that the efficiency of an electrically powered car is 2.5 times that of a gasoline-powered car for the conversion to mechanical energy. DATA: Energy content of 1 gallon of gas = 1.32 x10^8 Joules.
For Part A, we were to find the total electrical energy that the battery can deliver before needing recharged, but I was able to find that.

Homework Equations

[/B]
I really do not know what equation is necessary... F=ma or 1/2mv^2 maybe?

The Attempt at a Solution

[/B]
I am very stuck on the basic principles here. I believe I need to set up a ratio and then solve for mass, but what equation is necessary?

 

[PlatoDescartes]

Homework Statement

[/B]
A 12 Volt lead-acid car battery, engineered for "up to 500 or more charge/discharge cycles," has a rating of 330.0 Ampere-hours. It sells for $ 262.00.
Part B: The battery has a mass of 32.7 kg. What total mass of such batteries would be required to deliver the same effective mechanical energy as 16.0 gallons of gasoline? Assume that the efficiency of an electrically powered car is 2.5 times that of a gasoline-powered car for the conversion to mechanical energy. DATA: Energy content of 1 gallon of gas = 1.32 x10^8 Joules.
For Part A, we were to find the total electrical energy that the battery can deliver before needing recharged, but I was able to find that.

Homework Equations

[/B]
I really do not know what equation is necessary... F=ma or 1/2mv^2 maybe?

Update: I know that 16 gallons of gas is equal to 21.12 x 10^8 J and I am trying to figure out what m (mass of batteries) would deliver the same mechanical energy as that. Therefore, I need some equation to set equal to that to solve for work... Would W=21.12 x10^8 J= charge x change in voltage= F x displacement..?

The Attempt at a Solution

[/B]
I am very stuck on the basic principles here. I believe I need to set up a ratio and then solve for mass, but what equation is necessary?

 

[NTL2009]

F=ma or 1/2mv^2 maybe? ... update...

No, I don't think so. Focus on calculating the amount of energy in 16 gallons of gasoline, multiplied by the 2.5x factor of efficiency. Then calculate how many watt-hours a battery would need to deliver to provide the equivalent energy. Watt hours is amp-hours times voltage.

They are not asking you to calculate how much energy it takes to move the car, just the battery <-> gasoline equivalents. Once you have the battery watt-hour number, calculate battery mass from that.

 

[PlatoDescartes]

F=ma or 1/2mv^2 maybe? ... update...

No, I don't think so. Focus on calculating the amount of energy in 16 gallons of gasoline, multiplied by the 2.5x factor of efficiency. Then calculate how many watt-hours a battery would need to deliver to provide the equivalent energy. Watt hours is amp-hours times voltage.

They are not asking you to calculate how much energy it takes to move the car, just the battery <-> gasoline equivalents. Once you have the battery watt-hour number, calculate battery mass from that.

That makes sense; thank you!

 

[Davy_Crockett]

...And include the battery's 500 discharges vs. the 16 gallons of gasoline once only discharge (the question doesn't specify over what period the effective mechanical energy must be delivered)

 

[NTL2009]

...And include the battery's 500 discharges vs. the 16 gallons of gasoline once only discharge (the question doesn't specify over what period the effective mechanical energy must be delivered)

I don't agree. I think that was just extra info, for the student to decide whether it is relevant or not, and/or maybe included for a follow up question not listed here.

A battery is essentially a "container" for energy. The equivalent in a gasoline powered car is the gas tank. If we allow for "refilling" the battery for its useful life, we need to allow for "refilling" the gas tank for its useful life (many thousands of times before it might rust out?).

 

[Davy_Crockett]

Agreed. That calculation should be included when solving for the weight of fuel vs. the weight of battery.

While this is a good physics problem, it specs gasoline vs. a lead-acid accessories battery for an EV application.
Fine if your class of '78. But it would leave today’s classroom with a distorted perspective that some may carry for life.

Better to ask them to determine the volume of the phone battery in their pocket and then compare the energy density on the spec sheet to an equivalent volume of gasoline.

More realistic givens imo are: "1000 charge/discharge cycles" and "the electric motor is 4 times the efficiency of the ICE"