# How many grams of explosive are equivalent to the energy in a battery?

In the movie Terminator 3: Rise of the Machines, Arnie's fuel cells were twice shown to be extremely devastating when their stored energy was released.

In real life, how many grams of, say, gunpowder or TNT are equivalent to the energy stored in

1. An AA alkaline battery
2. A laptop battery
3. An electric car battery

Would the batteries be as devastating as the explosives if the energy could be released all at once (within milliseconds, say)? Presumably the power of chemical explosives come from the volume of gas they release...

One alkaline AA cell has about $11\,\rm kJ$ of energy. For a laptop battery, it is $360\,\rm kJ$. Chevrolet Equinox fuel cell has $58\,\rm MJ$ of energy.

One kilogram of TNT carries about $4.184\,\rm MJ$ of energy. Divide the numbers from the previous paragraph by this constant to see that the AA cell, laptop battery, and electric car battery have $2.6\,\rm g$, $86\,\rm g$, or $14\,\rm kg$ of TNT. Note that TNT usually releases all the energy abruptly.

Gunpowder has $3\,\rm MJ/kg$ or so. It means you have to add about $35\%$ to get the right estimate for the mass of equivalent gunpowder.

If you could release the energy from the batteries very quickly, the explosion could be equally devastating as the corresponding gunpowder and TNT except that batteries can't release energy this quickly.

• One AA battery doesn't have 11 kJ. They differ in real life, but for retail alkaline AA batteries, we're talking about 2.2 to 4.8 kJ. – Alan Rominger Sep 19 '12 at 19:38
• Dear alan, click at my 11kJ - I provided a source for my claim, unlike you. – Luboš Motl Sep 20 '12 at 5:10
• en.wikipedia.org/wiki/AA_battery#Chemistry_and_capacity. Capacities are rather variable but Luboš's value of 11kJ for an AA alkaline battery seems about right. – John Rennie Sep 20 '12 at 10:10
• Sorry, the 11 kJ would be in the range of Alkaline or Li-FeS2 batteries as per Wikipedia en.wikipedia.org/wiki/AA_battery. The link given for the 11 kJ, however, gives me 22-23 kJ for all of the mouse models by multiplying (J/day)*(months*31). – Alan Rominger Sep 20 '12 at 13:12
• @AlanSE At the footer of the first page it says: "*Avg energy in 1 AA Alkaline cell approx. 11KJ". – mmc Sep 21 '12 at 11:38

A battery's energy capacity is normally quoted in Amp hour, (or $\rm mAh$) the number of amps it could (in theory) supply for an hour. If you multiply this by the voltage you get energy.

Specifically, if you multiply by $3600$ seconds in an hour you get Joules.

A NiMH rechargable AA cell is about $2200\,\rm mAh$ and is $1.2\,\rm V$:

$$2200\,\mathrm{mA} \cdot 3600\,\mathrm{s} \cdot 1.2\,\mathrm{V} = 9.5\,\mathrm{kJ}$$

A Li-Fe 3.7v cell is about 3x more energy.

According to wikipedia a classic hand grenade contains 50g of TNT. Since TNT contains about 4KJ/g this is an energy content of 200KJ. So a grenade contains 20x as much energy as a regular AA cell or 7x as much as Li-Fe one.

• Nice, but you left out the explosives. – Cees Timmerman Nov 19 '14 at 15:43