### How Much Gas to Charge an iPhone?

I got a link to an interesting article recently, How many gallons of gasoline would it take to charge an iPhone?. The article was published on ExxonMobil's Perspectives blog. It was an attempt to put into perspective just how much energy there is in gasoline, and why it's so useful as a fuel.

Early on, the article presented a 'fact', without any rationale to back it up:

All of the energy concentrated in one gallon of gasoline is enough to charge an iPhone once a day for almost 20 years.

So, I thought I'd run some numbers to see just how reasonable this was.

First, what's the energy content of a gallon of gas? According to Wikipedia's Energy densities page, the energy density of gasoline is 47.2 megajoules per kilogram. A gallon of gas weighs about 6 lbs, for a mass of about ~~13.2 kg~~ 2.73 kg. Multiplying by the energy density gives ~~623.04 MJ~~ 128.73 MJ in a gallon of gas.

Now, for something that took a little more work, what's the energy content of the iPhone battery. According to Wikipedia's iPhone 4 page, the battery is 3.7V at 1420 mAh. (An Ah is the "the electric charge transferred by a steady current of one ampere for one hour" - Wikipedia). So, doing a simple calculation on that, let's figure out the power the battery is putting out, and then how much energy that would be after the one hour for the Ah:

P = IV

P = 1.42A * 3.7V

P = 5.254W

As a sanity check, that's in line with what some random guy on the Internet claimed on Yahoo Answers, according to his kill-a-watt power meter.

And since energy is equal to Power times time:

E = Pt

E = 5.254W * 3600s

E = 18,914.4J

So, if we simply divide the energy content of the gas by the energy content of the battery, we get ~~32,940 charges~~ 6806 charges. Assuming a charge every day for a year, that's ~~90.2 years~~ 18.6 years. Now, of course, there are inefficiencies in the systems, so that's not right. Gasoline engines in cars are typically on the order of 25% - 30% efficient (per Wikipedia), and their alternators are typically on the order of 50% - 60% efficient. However, permanent alternators run optimally can have efficiencies in the high 90%'s (again, per Wikipedia).

So, the claim that there's enough energy in a gallon of gas to charge an iPhone every day for 20 years seems pretty reasonable (in reality, when you look at the efficiencies, you won't be able to put all that energy into charging the phone).

An iPhone may not be huge, but 20 years is a pretty long time. It really just goes to show how much energy gasoline contains, and why it's so useful for powering vehicles.

As a side note, this is why I personally think that biofuels offer so much hope. If a way can be found to efficiently convert biomass into a gasoline like fuel (such as some of the studies on algae), we'd have a high density energy source that could take advantage of existing infrastructure. No waiting overnight to charge batteries - just a quick 10 minute stop at the pump to fill up with dead algae.

**Update 2012-05-08** As a reader pointed out, I made a boneheaded error in my conversion from pounds to kilograms (stupid metric system). I corrected it, striking through the wrong numbers and replacing them with the correct ones.