Here. Well, we will determine how long you must run in order to burn off £1 of fat, which is assumed to be 3500 food calories. What many people don't realize is that 3500 is actually in kilo calories. It's a little bit confusing because that is usually written as a calorie with a capital C. But it really is 3500 times 1000 times more calories. And in order to convert that to jules, There are four points 184 jules per calorie. Little calorie. Okay, so the idea is that we know the power at which the energy is getting expanded and we will assume that coast right into the fat, which may not be perfectly true, but we have basically Q dot times delta T in seconds is equal to that for amount of calories. Because we have the power in watts. We do want the uh energy in jules because a lot is the same as actual per second. Yes. And that's a lot of jewels, 1.4, 6 Times 10 to the 7th jules. A jewel, by the way is a very small unit. Um so therefore we can solve for the time to burn that off, simply divide that by the rate in jewels per second. And we get of the order of 11,000 seconds which if we convert that two hours, we see that it's about three hours, a little bit over. So 3.15 hours. And the question is this a reasonable plan. Well, um, most people would have a hard time running at that metabolic rate for three hours if you're a trained runner doing a marathon. Yes, you can expect to be doing that. But usually people do not run to burn off fat. They're doing it for other reasons. So that does not seem very reasonable. uh the next thing that's really interesting is that 80 of the heat that is generated over that three hours Um sorry, 80% of the energy that comes out during that three hours is in the form of heat. So the question is, where does that heat go? And of course this is why you sweat the heat generated. Uh huh. Goes to evaporation. And so we want to pretend that that sweat is water and how much evaporates During the three hour run. Okay, so we're going to take the metabolic energy. And the rule of thumb is that 80% of that goes into heat. And we're running for 11,400 seconds. Yeah. And that will give us the energy and jewels uh Using Q equals m latent heat of vaporization during a phase change. We are going to assume that the temperature of the water is of course, raise to the evaporation point. So we won't use any of it um to raise it up. But we'll just go ahead and use the latent heat of vaporization. That's a little bit over simplification. We could make this more complicated by, first of all raising the temperature From body temperature 200°C. Um Oh, we will use as the latent heat of vaporization for water. Yeah, let's see. That is a well known quantity And it is two for two Times 10 to the six jules per kilogram, roughly. Okay, so using that we can determine the mass that evaporates again. This is a little bit simplistic but will give us a good estimate. Um and that is roughly 4.8 We'll say 4.78 kilograms. Okay, And we can do some things with that to make it feel a little bit better or understand it a little bit better. 4.78 kg has a weight Roughly 2.2 lb per kilogram, So that's a little bit over 10 lbs. Almost 11 lbs. Of course you're going to replenish that by drinking water as you're running. But most athletes will tell you that the weight loss that they experienced during a heavy athletic activity, basketball game, football game, etcetera, that most of that weight loss is due to the fluids rather than the fat that goes away. Um We can convert this into leaders by using the density of water. Um So what is the volume? Um Mass per unit volume? Uh huh. Okay. Is equal to the density which is 1000 kilograms per cubic meters. And so we can solve for the volume is mass Divided by 1000 than cubic meters. Mhm. Okay, so this is roughly um mhm. Mhm is 4.78 Times 10 to the -3 m3. And then we can convert that into leaders by multiplying By one leader is 10 to the -3 cubic meters. So that is almost five L which again seems a little bit mhm. Yeah, overkill. And again most of it gets replenished as the person is running. But yes, it does point out that most of the mass that you lose in doing these activities is the fluids in your body.