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.

Fermi's Big Gulp

So we already guessed how much the Flash would have to eat but what about breathing? He needs air to turn all that food into energy. Would he use up the entire atmosphere?




Ok. Some backup science info. Energy release is controlled by mitochondria and the production of ATP through the Krebs cycle. It seems fairly complicated to me but in essence the most important thing for accessing all the stored chemical energy in the food is the oxygen intake and the carbon dioxide output. The hydrocarbons in our food get split up and carbons are oxidized into C0_2 and a bunch of water reactions are also needed to make this happen BUT the point is we really do basically burn the hydrocarbons that we eat.

Chemical reactions are all about exchanging electrons. Remembering that we are estimating: typically, when one electron is exchanged between two atoms there is an energy release of about 1.5eV. The units eV stand for electron volts and their just a convenient unit for \textbf{energy} when electrons are involved. To convert to everyday joules just know 1eV = 1.6 * 10^{-19}J = 2 * 10^{-19}J.

And one last thing: Most everyday hydrocarbons are just long chains of CH_2.

Food for Thought

Let's answer this in three parts. How much energy does the average American consume, how much does that cost, how much does each calorie cost and how much energy would the Flash need.

There's a number of ways we could estimate how much one person spends per month for food. You could say that you eat out every meal (3 times a day) at some fast food joint for $10 a meal. That kind of life style has a monthly bill of 30 * 3 * 10=$1000 per month. I think that's high at $30 per day. What about $1 per day? At that price food would only cost you $365 each year. Ya right. So the easy numbers between $1 and $30 are about $10 per day or $3 per day. Let's be nice to Wally and say $3 per day or about $100 per month.

So we've guessed it can costs about $3 a day to eat (I know it seems low). Now we must guess how many calories you consume a day and so find the cost of every calorie.

How many calories do you eat per day? Maybe you know this maybe you don't. If not, maybe you know how many calories are in a McDonald's Value Meal (1167 cal) or in a can of coke (200 cal) or in a steak (500 cal). Therefore, you eat more than 1000 cal and probably not 10,000 cal. So then we guess the geometric mean which is 10^{7/2} = 3000 cal per day. So let's convert from calories to Joules (there's 4200 Joules in every calorie). 3000 cal/day * 4000 J/cal = 12 * 10^6 J/day. A physicist like Ray Plamer or Reed Richards would be happier if we turned this to Watts. Watts are Joules per second. So as a side note the power usage of a human being is 12 * 10^6 J/day * day/24hr * hr/60min * min/60sec = 150 W. Oh good - more power than a lightbulb.

So anyway that was a sidequest. The important thing is that a person consumes 3000 cal or 10^7 J everyday. Plus spends $3 a day for that food. That means that $1 will buy you 1000 cal or 4 * 10^6 J.

Next we have to estimate how much energy the Flash needs. Let's guess that most of his energy goes to running (that way if our answer is small compared to a normal person we can add the energy of a normal person to it or if our answer is big compared to a normal person we know that it is insignificant). The energy of him running is kinetic. We already used the equation for kinetic energy KE = 0.5 * m * v^2. If we allow for fictitious elimination of frictitous forces then if we can guess his speed, we will know the energy needed to get him to that speed. He needs that much energy every time he runs to that speed. Remember we are guessing for an average day, not at his fastest nor his slowest.

The speed of light (3 * 10^6m/s)?. %1 the speed of light? The speed of sound (300 m/s)? The speed of thought (only about 100m/s since it depends transport mechanisms of ions crossing membranes)?

Let's guess that he goes 10 times the speed of sound for an average run. The energy he needs to reach that speed is KE = 0.5 *m * v^2 = 0.5 * 100kg * (10 * 300m/s)^2= 0.5 * 100 * 9 * 10^6J=5 * 10^8J.

Since he needs that much energy every time he gets to those speeds we need to ask how often does he go that fast? We are talking about a cocky jock with a fairly large rogue gallery. So let's say he goes more and once a day but less than 100 times a day. The geometric mean: 10 times.

Then the energy the Flash needs for running in a day is 5 * 10^9J. At a price of $1 for every 4 * 10^6 J, the Flash must spend 5 * 10^9J / (4 * 10^6 J/$1) = $10^3 = $1000 more per day than muggles.

We said that a single person could eat for $100 per month and based on that the Flash's monthly grocery bill is $30,000. That's more than some of use make in a year! Notice that if we had said that Wally ate out for every meal his bill would be 10 times greater. A bright supervillain interested in discovering the Scarlet Speedster's secret identity might begin by looking for abnormally large grocery bills.