When I attempt to calculate the O2 necessary for a day of metabolism at rest (for an imaginary average human) and compare it with the expected O2 consumed per day my results differ by a factor of 3. I don't expect it to be 1 to 1, but a factor of 3 makes me think that I am missing a fundamental concept.
For our fictional human, I'm starting with the values for 1 MET. Specifically:
- RMR (kcal / kg / hr) = 1
- VO2 (mL / kg / min) = 3.5
I then define the weight of my human:
- weight (kg) = 70
- RMR (kcal / hr) = 70
- VO2 (mL / min) = 245
And convert to more useful units:
- RMR (kcal / day) = 70 * 24 = 1680
- VO2 (L / day) = 245 * 60 * 24 / 1000 = 352.8
At this point, my understanding is that consuming 352.8 L of oxygen should produce somewhere in the ballpark of 1680 kcal at rest. My next assumption is going to be that aerobic respiration of glucose is accounting for all of the energy throughout this day of rest. I'm aware this isn't reality, but I wouldn't expect it to be 3x off. I'd guess that either this assumption is wrong or I'm misunderstanding something in the following math.
Let's start with some more constants regarding cellular respiration.
- ATP creates 7.3 kcal / mol
- An average of 30 ATP are generated per glucose (glycolysis, krebs, etc)
- 6 O2 are required to aerobically metabolize 1 glucose
Given the energy to ATP ratio, we can compute the ATP necessary per day. I should note that the result here is about twice as high as reference numbers I've seen so I am suspicious.
- ATP (mol / day) = 1680 / 7.3 = 230.1369863
- Glucose (mol / day ) = 230.1369863 / 30 = 7.671232877
- O2 (mol / day) = 7.671232877 * 6 = 46.02739726
To convert the O2 requirements for our ATP from moles to liters, we use Avogadro's law at standard pressure (100 kPa) to conclude there are 22.712 liters per mole in a gas.
- O2 (L / day) = 46.02739726 * 22.712 = 1045.374247
And finally, we can see that my calculation says that you need 1045.37 liters of oxygen to produce 1680 kcal of energy through aerobic respiration, but earlier I computed that you should only need 352.8 liters using 1 MET as my basis. There were assumptions made in there, but these results make me think that I am still misunderstanding a fundamental concept.