eli5: Why are charged batteries heavier than empty ones?
In: Chemistry
E=mc^(2). Energy has mass.
That said, the amount of additional mass is so small that it might as well not actually exist for any practical purposes. For instance, consider something with a huge storage capacity like a Tesla Powerwall. It can store 13.5 kWh, which translates to 4.86*10^7 Joules. That’s enough energy to fully power the average home for something like 16 hours.
If you rearrange the above famous equation to solve for mass, you get:
m = E/c^(2)
Now let’s plug in some numbers:
m = 4.86*10^7 J / (2.998*10^(8) m/s)^2
Once we solve that equation, we discover that the fully charged Powerwall weighs an additional 0.54 micrograms. For comparison, that’s about half the weight of a single grain of baking powder. The Powerwall’s weight fluctuates order of magnitude more from random dust particles landing on it than from being charged.
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As an aside, this might give you some insight into why nuclear bombs are so powerful. 0.54 micrograms worth of mass is equivalent to the energy needed to power your home for 16 hours. The bomb dropped on Hiroshima converted about 700 milligrams (700,000 micrograms, less than one-third the mass of a U.S. dime) of mass to energy. If we use the same metric, that’s enough energy to power your home for over 2,500 **years**.
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