Fine Structure

Electrons per Song on an iPod

Perusing the newest Apple hardware teardown on iFixit this morning, I noticed a curious statistic about the new iPod Shuffle. No, not that it weighs a measly 10.7 grams (I'm not sure if this is a benefit or simply a guarentee that you'll loose it) or that it holds a thousand songs (more than you could ever listen to on a quick run or even five quick runs, I imagine). According to iFixit, the new shuffle has the itsybitsiest battery of any iPod, ever. It's only rated for 73mAh (milliamp-hours) at 3.7 volts. And, in some weird testament to their IC design, it still runs for approximately 10 hours. That's a really tiny and yet incredibly long lasting battery.

So this got me thinking about just how much power is stuck in this tiny machine. And does a smaller package necessarily mean we're using less power? Or simply that technology allows us to pack the same power into less space? And finally, the important question of the morning...

Just how many electrons does it take to play a song on a new iPod Shuffle?

(Looks like LaTeX broke with the move to the new server so we're on our own for this one)

According to iFixit, the battery is 3.7v @ 0.073A•h (73mA•h) and Apple says that the new shuffle will play tunes for 10 hours straight. So how can we tell how many electrons we have?

An amp is a measure of electrons per second; 1A is about 6.424•1018 e / s which means that the total number of electrons per 10 hours at 1A is about 2.247•1023 (we're just multiplying by 60 • 60 • 10). Scaled down to the actual battery rating (0.073A, if you recall), we get around 1.64•1022 electrons. That's the total number of electrons that this ideal iPod battery can discharge through the electronics. At approximately 4 minutes per song (Apple's average), we can play through 150 songs in 10 hours (far less than the 1000 song storage capacity), giving us approximately 1.09•1020 electrons used per song.

Well, that's... a fair number? Actually we have no clue what that number means because we're mostly in the dark about how many electrons it costs to do just about any other daily electronic task. While I would love to give a run down of every electrical item in a common household, I think it's fair to simply compare iPods for today.

Which iPod is most electron-efficient?

Using the same calculation, here's what I calculated for a number of current iPods:

As could be reasoned fairly, the more junk you stuff into an iPod, the more electrons it takes to play a song. These iPods have some interesting incremental power requirements (screens, then non-flash drives) which we could continue digging into if we had the time. For now though, we'll leave it at this. Use this information wisely when determining how electron-friendly you'd like to be when using your iPod!

Comments

I guess Apple should market the Shuffle as the greenest iPod ever!

March 18, 2009
1:40 AM

From Rajat

Another thing to consider is that you can do tasks with fewer electrons if you have a larger potential in the battery. Looks like the iPod is pretty well standardized on 3.7 V, though, so the comparisons are good.

March 29, 2009
2:23 AM

From Tom

That's great! But a minor point: where do you get 6.424 x 10(18) e / s from at the start? Shouldn't it be the reciprocal of (according to a Google of "electron charge") 1.60217646 × 10(-19) = 6.24 x 10(18) e/s i.e. one coulomb per second?

Or am I missing something (a stong cup of coffee, for example).

Either way it doesn't alter things much. Fascinating calculation. Thanks!

April 14, 2009
12:48 AM

From chrisw.myopenid.com

Hi Chris,

You're completely right. I have an ampere defined in my notebook as 6.424 • 10(18) although looking up the definition in a couple places right now sets it as 6.24 • 10(18). Perhaps I got a bad approximation or just jotted down the wrong number? I'll update all the calculations when I have a free moment. Thanks!

April 14, 2009
3:51 PM

From Nick

this is awesome.... nothing better then random facts at 6:30 in the morning, no wonder Im getting a degree in physics.. i need a girlfriend lol

April 17, 2009
3:36 AM

From bryan