Question

1. A 1 liter bottle of Coca Cola weighs about 1 kilogram. If that bottle were combined with an equal amount of anti-Coke (i.e. Coca Cola made of anti-matter) so that both liquids annihilate and get transformed into pure electromagnetic energy (gamma rays), how many Joules of energy would be released? (note that you get the units in Joules if you use units of kilograms, meters and seconds for your calculations.) 2. The nutritional (chemical) energy content of the same amount of Coke (e.g. 2kg or 2 liters), which is the total content of calories that you can read in the nutrition facts label (note: 1 food calorie 4,186 Joules). How much larger or smaller is that energy than your answer to #1?

Answer 1

1.

$\text{total mass}=m=1+1=2\text{kg},\\ c=3\times 10^8\text{m/s},\\ \therefore E_{nuclear}=mc^2=2\times (3\times 10^8)^2,\\ E_{nuclear}=18\times 10^{16}\text{J}.$

2. 2 liters of coke is equivalent to 777.78 calories. 1 calorie =4186J.

$\therefore E_{chemical}=777.78 \times 4186=3.25\times 10^6 \text{J}.$

Now

$\frac{E_{nuclear}}{E_{chemical}}=\frac{18\times 10^{16}}{3.25\times 10^6}=5.54\times 10^{10}.$

Therefore, for coke, nuclear energy is $\approx 10^{10}$ times greater than chemical energy