# Cost of driving: electricity vs. gasoline

1. Jun 4, 2008

### Wordsmith

Hello All,

I'm trying to get a sense of the cost of using electricity e.g., plug-in hybrid vs. the cost of operating the same vehicle using gasoline. I've read a comparison using the btu value of gasoline vs watts/btu but I'm not sold on that idea since the vast majority of thermal energy in an automobile goes out the tailpipe. What I was thinking of was choosing a 'standard' car like a Ford Taurus, operated on a highway at a steady state for one hour. Using horsepower as the common denominator between gasoline and electricity As far as gasoline consumption, I would propose dividing the miles travelled in the hour by some reasonable highway MPG. Just for sake of example, I have read that steady-state 50 MPH driving uses 40 HP. Figuring 25 MPG highway, gasoline at $4.00/gal and electricity (746 W/hp * 40 hp. for one hour = 29.84 KWH. At$0.10/KWH, driving the 50 miles cost $2.98 using electricity or 2 gallons of gas =$8.00.

Obviously, the example is greatly simplified, but is it a fair comparison?
Wordsmith

2. Jun 5, 2008

### Staff: Mentor

You are right that most of the energy goes out the tailpipe. The efficiency is somewhere around 30%. The easiest way to deal with that is to divide the fuel economy by the efficiency to find the equivalent economy of a plug-in hybrid.

Ie, a car that gets 40mpg would get an equivalent 40/.3= 133 mpg.

There are certainly other complicating factors, but that should get you in the ballpark.

3. Jun 5, 2008

### RonL

Although I don't agree with all he says, there are a lot of things worth considering in this presentation.

It might be a little help to some.

http://ludens.cl/philo/electric.html

4. Jun 7, 2008

### rbj

this looks interesting. even though i am an electric car advocate (and had been for some time), i am not sure that i disagree with this guy (the author, Manfred Mornhinweg, XQ2FOD, looks like he's an amateur radio operator licensed in Chile) about the facts.

when you take a Thermodynamics course in mechanical engineering, you will learn about the ideal Carnot Cycle, entropy, and the difference between "high-grade energy" (ordered mechanical energy such as the twist of a shaft or electricity) and "low-grade energy" (essentially heat). when converting from Joules of heat to Joules of ordered mechanical energy (via an ideal Carnot Cycle), there is a theoretical maximum efficiency of

$$1 - \frac{T_{in}}{T_{exhaust}}$$

where the temperatures are relative to absolute zero, like Kelvin. so, if fuel is burnt to make electricity, the cost of a Joule of electriciy must cost more than a Joule of heat from some combustible fuel (by a factor of at least the reciprocal of that efficiency). so you have to consider the cost of the electric Joules compared to the cost of the gasoline Joules with figure divided by the reciprocal of the efficiency of the engine (from point of sale of the energy source to the axels of the drive wheels). that's how to compare these apples to oranges.

the reason why i might not agree with that ludens.cl guy is that i think that centralized power plants (where the chemical energy of a fuel is converted to heat and then to mechanical power) are far more efficient than the miniature power plants we drag around with us when we drive our conventional cars around (although the technology of both are getting better, but i think that the electric power plants' efficiency is closer to their limit than car engines).

5. Jun 7, 2008

### rbj

another cost you have to consider in the cost of a pure electric car, is the cost of replacing the batteries after their expected life. traction-motor batteries (deep-cycle rechargable batteries either lead-acid or of some modern technology like lithium-nickel) ain't cheap, and after some, i dunno, 10000 kilometers (maybe more, i dunno what the mean lifespan of a battery is, nor precisely the cost), you have to replace and responsibly recycle those batteries. that costs money. serious bucks.

6. Jun 7, 2008

### Shackleford

Yeah, like a couple grand if I remember correctly. So, the cost effectiveness drops drastically.

7. Jun 7, 2008

### LURCH

I have done considerable figuring on this topic, but took a very different approach from the one in the OP. I took numbers from the one highway EV that I know of (the Tessla), and multiplied the number of kW/h per mile by the price of electricity on my electric bill that month. My conclusion was that driving 25mi would require a certain amount of electrical energy (I think it was about 4kW/hrs; I'll look it up), which I then reffered to as an electric gallon, or EG. From my calculations, driving about on electrical energy would be about $1.00/USgal (that's assuming the electricity gets taxed like petrol, about$.40/EG).

I also figure the CO2 emmisions would be about 1/2 that of gas (and that assumes no improvement over current rates of CO2 per kW/hr).

Last edited: Jun 7, 2008
8. Jun 7, 2008

### rcgldr

Unless your source of electricity is from a coal burning plant.

9. Jun 7, 2008

### montoyas7940

How would CO2 emissions compare if it were from a coal burning plant?

10. Jun 7, 2008

### rcgldr

I don't know the exact numbers, but...

Coal is the major fuel used to generate electricity worldwide, but burning it adds more carbon dioxide, a greenhouse gas, to the atmosphere per unit of heat than does burning other fossil fuels like oil and natural gas.

http://www.america.gov/st/washfile-english/2007/May/20070530134219lcnirellep0.6537592.html

How toxic are the li-poly batteries used in electric vehicles? Can these be recycled? What's the loss in energy in having to produce electricity, transmit it, charge up batteries, which have to store it, then convert it into linear power to propel a car, as opposed to extracting, tranporting, and storage of gasoline, where all the conversion into linear power occurs within the car?

Last edited by a moderator: Apr 23, 2017
11. Jun 8, 2008

### LURCH

No, that's assuming the electricity comes from nothing but a coal-burning power plant, one with no better carbon control techniques than those currently in use.

12. Jun 13, 2008

### LURCH

Ah, here is that research I did:

As can be seen from this site...
http://www.teslamotors.com/efficiency/well_to_wheel.php [Broken]
...the Tesla requires about 110Wh to travel 1km. This translates to about 160Wh/m. According to the EPA, the average passeneger vehicle gets about 25mpg, so multiplying 160Wh/m by 25mpg, we get 4000Wh = 1gal. This is to establish what I call the Electric Gallon (or EG), which is the amount of electrical energy required to drive the same distance as 1 gallon of gasoline; 4 kWh.
Looking at my electric bill from last month, I see that I am paying about 10 cents per kilowatt hour, including all taxes and service fees. So...
$.10 per kilowatt hour times 4 kilowatt hours gives me about$.40 per EG. Of course, if electricity is being sold as fuel for vehicles, the taxes usually charged for gasoline will have to be charged for that electricity in order to maintain roads. Also, if gas stations begin selling electricity, the electric utilities will have to charge at a higher rate, due to the very high current the stations would require. And of course, the fuel stations themselves would have to mark up the price in order to make a profit. Depending on the state in which one lives, gasoline taxes can be anywhere between $.30 and$.50 per gallon...
http://www.energy.ca.gov/gasoline/statistics/gas_taxes_by_state_2002.html [Broken]
... and the national average is about $.40, bringing the price of electrical energy as automotive fuel up to$.80 per EG. So, even if the electric utility and the fuel distributor really gouge the customer at $.10 per Equivalent Gallon apiece, the price still only goes up to$1.00/EG.

It can also be seen from this DOE web site:
http://www.eia.doe.gov/cneaf/electricity/page/co2_report/co2report.html#electric
that burning coal to generate electricity creates about 2 pounds of CO2 per kilowatt hour. Multiplying by 4 kWh, this renders about 8 pounds of CO2 per EG. By comparison, according to this EPA web site:
http://www.epa.gov/otaq/climate/420f05001.htm
burning gasoline generates approximately 20 pounds of CO2 per gallon; roughly double the amount.

Last edited by a moderator: May 3, 2017
13. Jun 14, 2008

### Phrak

Nice research, Lurch.

I'd add that converting power from the mains to recharge the batteries obtains losses in both battery heat and power conversion, perhaps 15%.

14. Jun 14, 2008

### Phrak

Lithium batteries are still an evolving technology. In the form that I've read about, the lithium is in the form of an olivine, lithium iron phosphate; no heavy metals, which is nice to see. At one time I looking up electric power generation and transmission efficiency. I think 39% is close to nominal.

The cost of coal is about $100 per ton Nominally 20*10^6 BTU per ton (varies from about 16 to 26 MBTU) 1000 BTU = 293 Watt-hours about 39% efficiency for delivered energy from the mains ---------------------------------------------------------------- Cost in coal, alone, for delivered power: 4.4 cents per kilowatt-hr I would have guessed 6 to 7 cents out of 10. But the numbers do seem to be in the right ball park. So how does gasoline compare to coal in cost? Coal: 88 KBTU per dollar (using the 10c per KWhr figure) Gasoline: 125 KBTU per gallon, at$4.00 per gallon obtains 31 KBTU per dollar

Each delivers about 20 - 25% efficiency to the axle.

Last edited: Jun 14, 2008
15. Jun 16, 2008

### Littlepig

you are comparing a car's motor efficiency with a power plant efficiency...........

anyway, when doing some kind of effectiveness evaluation, you must know what the degree of accuracy you want. first you were only considering a first approximation of the equation: electric versus gasoline, then you start putting terms about battery, and then about effectiveness of electrical energy produced in power plants versus mechanical energy produced by the car with gasoline or with electrical energy. So, at this time, you have already some variables.

however the point is: if you want to know how you do the calc, is one thing, if you want to know what are the variables of it, is other thing... physics can give you both and can give you an equation relating every variable and the optimum solution(if it exists), but you have to say at what level of accuracy you want, otherwise, more some days and we are arguing that at your living place, energy chargers are at x miles, so you will waste more energy to go there than to a conventional fuel station...xD

16. Jun 16, 2008

### Phrak

I've done a little more reasearch in the mean time on coal fueled electric power generation. They are not as efficient as I beleved. Some years ago the hot technology was internal combustion coal dust turbines, but this technology doesn't seem to have made it to general use, so the less efficient boiler-driven steam-turbine seems to be the common motive source.

The efficiency of coal burning electric power generatation is about 35%.
The efficiency of delivery over the power grid (US) averages about 93%.
Overall efficiency. 0.35*0.93 = 32.5%

Last edited: Jun 16, 2008
17. Jun 22, 2008

### cspeaker

Has anyone ever considered the use of Geothermal driven power plants to generate the electricity for electric cars?
Yellowstone has enough geothermal energy to drive all the geothermal electric power plants we would ever need. The only cost would be for plant construction and maintenance. (I know it would require congressional approval to use Yellowstone.)
I can envision the government selling the electricity through separate meters with the electric cars being required to charge at night in order to receive the special pricing and not overload the grid. The revenue from the sales could be used to fund (pick your favorite unfunded liability) or reduce income taxes ... whatever. This would also result in zero CO2 emissions. The revenue could also be used to help lower income families purchase their first electric cars and get the older (cheap) gas hogs of the streets.

This could also be the initial step towards the fuel-cell cars with hydrogen being produced through electrolysis from this new found excess of electricity.

Last edited: Jun 22, 2008
18. Jun 22, 2008

### LURCH

Everybody, but that's a different thread, I think.
If you've alerady got the cars running on electricity that's produced with zero emissions, what do we need fuel cells for?

19. Jun 22, 2008

### OmCheeto

Adding together your numbers and my numbers, I come out with $1.92 for a 50 mile trip using solar power. 30 kwh required per trip 45 watts/panel 180$/panel
8 hours of sun a day
360 wh/day/panel
83.3 panels required
$15,000.00 cost of panels 13,036 miles driven a year 391,071 miles driven in a career(30 years)$0.038 $/mile over your career$1.92 cost of 50 mile trip

energy equivalent mpg at $4/gal: 104 mpg energy equivalent mpg at$5/gal: 130 mpg
energy equivalent mpg at \$10/gal: 261 mpg

assuming a lot of course

20. Jun 27, 2008

### GTrax

Some time back, in another thread, I did a estimate comparing what it would take to move my car through a journey if it were powered electric, working it back through all the stages to the power station.

Its not nearly as good as the varied research and approaches in this discussion, but I include the pointer here ..
https://www.physicsforums.com/showpost.php?p=1509048&postcount=46"

Last edited by a moderator: Apr 23, 2017