Is a short dip in a cold water really equivalent to 20 minutes of running?

I came across some article comparing a short dip in a cold water (2 mins) to 20 minutes of running in terms of the amount of calories burned. Would you suggest a way of doing an experiment that would prove/disapprove this claim (including way of measuring and equations)? I am an elementary school teacher and would like to work on this with my class of 8th graders as I think it could be fun. However, I am not sure how to approach this given the fact we have limited equipment and no advanced math.

The amount of calories burned while running is not a problem, but finding a way of measuring the energy consumption while in cold water seems quite tricky. From my own experience, the decrease of the body temperature after the ice dip lasts quite long (it takes me sometimes more than twenty minutes to get to the initial body temperature), therefore it rather shows that the calories burned are spread in a longer period of time and that the cold dip just shocks the system to start the heating process.

• There's no way the two are equivalent. They must be erroneously comparing calories with kilocalories of food (which are loosely called calories). Commented Feb 6, 2021 at 21:46
• Adding a reference to the article would be useful so we can determine what exactly is going on here Commented Feb 6, 2021 at 22:10
• Why is the former no problem? I have no idea how I would measure that, except for spending several weeks either with or without running, with everything else kept precisely the same, and cmparing the weight gain/loss. I think measuring calories burnt in any process in a human being is a difficult task. Unless you put them in a huge calorimeter and you have a good way of relating things. Commented Feb 6, 2021 at 22:43
• @NorbertSchuch The nominal amount of calories burned per mile of running is about 100 cal, Assuming 8 minute miles, you would burn about 250 cal in 20 minutes. Actually these are kilocalories, or 250000 thermodynamic calories in 20 min. Commented Feb 6, 2021 at 22:59
• @Miroslav You could try to measure how much the water warms up. This should give a zeroth order guess for the amount of calories which went from the body to the water. Then again, the way the body reacts to cooling is probably not that simple. Commented Feb 6, 2021 at 23:03

Google suggests that running burns roughly 15 kilocalories (often called "Calories") per minute, though it certainly varies depending on how fast you go, among other things. But let's take 300 kilocalories as a guess for 20 minutes of running.

One way to equate this to a dip in the water is to estimate how much of a body temperature change it represents. If you assume the heat capacity of a human is the same as that of water, then each kilogram of person takes one kilocalorie to change temperature by one degree. So to give up 300 kilocalories, the average body temperature of a 50 kg human would cool by 6 degrees. For an actual person, the cooling would be partially offset by internally generated heat. But if you imagined a person-sized chunk of meat at a person-like temperature, you could try to estimate how long it would have to be immersed in cold water to cool by an average of 6 degrees. I would guess it's longer than 2 minutes.

• If your body core temperature drops by 6 degrees, you're likely no more in a good state. Commented Feb 6, 2021 at 22:44
• @NorbertSchuch right, severe hypothermia Commented Feb 6, 2021 at 22:46
• Not sure you're still conscious if your body core temperature is somewhere around 32. On a different notes: Calories = Kilocalories in your answer? Commented Feb 6, 2021 at 22:47
• @NorbertSchuch yes Commented Feb 6, 2021 at 22:48
• @NorbertSchuch I use Calories, with a capital C, to represent a food calorie, otherwise known as a kilocalorie. It is not an error. Commented Feb 6, 2021 at 22:57