Why a Battery Weighs More When It’s Charged

It’s the middle of December as I write this. My backpack radio kit hasn’t had a good workout since I last took it out in the field for a Parks On The Air (POTA) session a couple of months ago. But, we got lucky with the weather one day this past week. The temperature got up to 14 degrees Celsius before strong winds brought in a Colorado low and took the mercury back down to the freezing zone.

I got a chance to set up as a “Backyard On The Air” station to test a new portable antenna I had built for next summer’s outdoor operating season. My Bioenno LiFePO4 battery was freshly charged for the occasion and I was eager to get out on the deck and fire up the rig to see how well the new antenna would perform.

The Common Cold virus had invaded my bloodstream and I was feeling a little weak as I picked up the backpack containing my Yaesu FT-891 radio, a homebrew L-match tuner, the Bioenno battery and various cables and accessories that I like to carry with me on a field trip. “Strange” I thought, “this backpack feels a little heavier than usual”.

Maybe it was just the debilitating effects of my mild illness that was affecting me, but I wasn’t sure. Then suddenly I had one of those “light bulb moments”. “Of course” I thought, as my university Physics training began kicking my brain into high gear, “I just charged the battery, so that is obviously the reason the backpack feels heavier than usual”.

Now most people have probably heard of Albert Einstein’s famous energy/mass equivalence equation, E=mc^2. It may not have much relevance to most people’s everyday lives. Not so for me. From my teenage years I was on a path toward a lifetime of science awareness. I vividly recall my high school physics teacher’s erudite response to a student who complained that his pen had disappeared. “Don’t be silly boy; if your pen had disappeared the whole city would be lying in ruins”.

Do the math yourself. Take the mass of an average pen and multiply it by the square of the speed of light. That’s one heck of a lot of Joules to unleash on an unsuspecting city. Old Albert had hit the nail squarely on the head with his E=mc^2 equation.

Einstein’s genius was further driven home to me when I started my freshman year in college. A bunch of long-haired 1970s yahoos had to be indoctrinated into the wonderful world of Physics. And the faculty staff had a cunning trick to do just that. Teach those long-haired kids how to make an atomic bomb! In fact, teach them all of the different ways to build an atomic bomb. Just keep those long-haired weirdos away from any source of Uranium or Plutonium.

We did have a radio-isotopes laboratory in which we could indulge our fantasies of playing god with the World. Special clothing had to be worn when we entered the lab. When we left the lab we had to undergo a full-body scan with a Geiger counter to ensure we were not sneaking any dangerous isotopes out with which to create criminal mischief. The local police were familiar with our penchant for mischief so every caution was very well advised.

And so it it dawned on me; at last I understood why my backpack radio kit seemed heavier than usual – I had just charged the battery! I know; you are getting a bit skeptical around about now. “This idiot must be enjoying a little bit too much of the old ‘Scottish Champagne'” you may be thinking. You may be right, but trust an old Physics grad; the mathematical proof is in old Albert Einstein’s equation.

My Bioenno battery is rated at 12Ah and although it puts out over 13 volts most of the time, let’s call it a 12V battery. Whatever number we calculate for the increased weight can then quite honestly be claimed to be a conservative number.

So here we go;

A 12V battery with a storage capacity of 12Ah holds 144Wh of energy.
1 Watt = 1 Joule per second
So 144Wh = 144 x 3600J = 5.18400 x 10^5 Joules

Using Einstein’s mass/energy equivalence equation, E=mc^2
E/c^2 = 5.184 x 10^5/(3 x 10^8)^2
= 5.184 x 10^5/9 x 10^16
= 5.76 x 10^-12 Kg
= 5.76 x 10^-9 g
= 5.76 nanograms

Alright, a handful of nanograms isn’t a whole lot, but when you’re out hiking to a radio spot at the top of a steep hill on a hot humid day, where do you draw the line? Quod Erat Demonstrandum!