Calculating the VO2max of an orange

[00:00:00]we'll be calculating the VO2 max of an orange.

[00:00:04]And although Garmin, you can kind of trick it into calculating a heartbeat for this orange, it won't give you a VO2 max score.

[00:00:12]But, we can use some high school chemistry to get an estimate of what the VO2 max score of an orange would be.

[00:00:19]If you don't know, VO2 max is essentially an indicator of aerobic fitness. So, the untrained adult male might have a VO2 max of 35 to 40, while trained athletes might exceed 60, and the highest ever recorded VO2 max by a triathlete, Blummenfelt, was 101. So, crazy stuff. But, VO2 max is how much oxygen your body can consume maximally. So, what is the maximum rate of oxygen that you can take, and it's in uh the units mg per k per kg per hour.

[00:01:02]Um So, how would we begin to calculate the VO2 max of an orange?

[00:01:07]Well, scientists have done experimentation, and they've calculated that at room temperature, or 20° C, 293.15 K, a sweet orange releases 12 mg of CO2 per its body weight, kg, per hour.

[00:01:35]Now, that's a critical piece of information to calculate the VO2 max, um because how would um a fruit like this consume oxygen? How would we determine that? Well, there's a well-known equation for cellular respiration. To stay alive, the orange has to convert um simple sugars.

[00:01:58]So, C6H12O6, that's glucose. It uses up the oxygen.

[00:02:04]That's how we're measuring its aerobic fitness.

[00:02:07]And then, CO2.

[00:02:10]To produce carbon dioxide and water.

[00:02:14]This equation, it's balanced, is known as cellular respiration.

[00:02:18]And you can see that the moles of O2 going in are the same as the moles of CO2 coming out. So, this tells us that VCO2 equals VO2.

[00:02:30]And that means to calculate the VO2, we only need to look at the VCO2, which we can calculate after a bit of work from this critical piece of information here.

[00:02:41]So, in order to investigate this, it's more helpful to convert the milligrams into moles.

[00:02:48]So, we know that uh carbon dioxide, it's a 40 44.01 g equals 1 mol uh for carbon dioxide.

[00:03:02]So, to convert this to moles, it's essentially just 12 divi- mg.

[00:03:08]Notice that this is g, so we have to convert 44010 mg.

[00:03:15]Cancel. That's the number of moles uh of CO2 per kg per hour.

[00:03:27]All right. This value is approximately, let me see, 0.002727 moles per kg per hour.

[00:03:42]All right.

[00:03:43]And now, we can use the ideal gas law to find the the V, the volume.

[00:03:50]We have the equation PV = n r t.

[00:03:55]Well, P is pressure. We'll keep that at one atmosphere.

[00:03:59]V is what we're trying to solve for.

[00:04:01]N, that's the number of moles, which we just calculated that an orange produces uh per kilogram per hour.

[00:04:10]R is the ideal gas constant. I think it's around.08 um atmospheres for every mole times K.

[00:04:23]So, it's a constant. And then T is the temperature, and we're taking room temperature, so that's 20 C or we're going to use 293.15 K.

[00:04:35]Units are always supposed to be in Kelvin.

[00:04:37]So, plugging all of these known values in, you should get that V equals um.00 656 L or liters or roughly 6.56 mL of O2 per kilogram per hour. And VO2 is typically displayed in kilograms per minute. So, to get the VO2 of an orange, we simply divide by 60 minutes.

[00:05:09]And then that gets us the VO2 of an orange is roughly around 6.56 / 60, which equals.109 mL divided by kg per min.

[00:05:27]All right.

[00:05:28]That is a very low VO2. So, the orange is a pretty aerobically unfit fruit.

[00:05:37]Maybe after some training it can develop its VO2, but that has yet to be tested. All right. Thank you.