2009-09-06

Flash Forward a Billion Years

So we are going to guess how much oxygen the Flash uses each day.

As a few reminders:
   (1)The hydrocarbons in our food get split up and carbons are oxidized into C0_2 meaning we really do burn the food we eat.

   (2)Typically,there is an energy release of about 1.5eV when one atom exchanges an electron with another. The units eV are related to joules by 1eV = 1.6 * 10^{-19}J = 2* 10^{-19}J.

   (2)Food is mainly composed of long chains of CH_2. When it is decomposed to get the energy it holds the carbon binds to two oxygen and the two hydrogens bind to a single oxygen meaning there are TWO reactions for every CH_2 which need THREE oxygens.

We already found that the Flash uses 5 * 10^9J per day. How many reactions is that? Turn joules into electron volts and divide by 1.5eV for every reaction:
5 * 10^9J * (1.5eV / 1.6 * 10^{-19}J) = 5  * (1.5/1.6) * 10^{28} = 5* 10^{28} reactions.

And we said 3 oxygens for every 2 reactions means we need 5 * 10^{28} * 3/2 = 7 *10^{28}$ oxygens per day.

That sounds like a lot but is it really? There's 6 * 10^{23} atoms in every mole and oxygen is eighth on the periodic table which means 1 mole weighs 8 grams. So then the Flash goes through 7 * 10^{28}  *  (1/6 * 10^{23}) * 8g = 8 * 10^5 g = 800 kg of oxygen each day. WOW but wait a minute...

In the last question we found that there's about 10^{18} kg of oxygen in the atmosphere. Which means it would take the Flash 10^{15} days or 3*10^{12} years or 3000 billion years.