Tuesday, 7 August 2012

Simple thermodynamics

I forwarded Alex Hutchinson this and this article regarding 'cooling off with hot drinks'. I was pleased that he posted the pieces, but I feel responsible for complexifying something people weren't event that worried about in the first place: the temperature of their beverages during exercise.

To backtrack, the premise is that if you ingest a warm beverage on a hot day, the extra heat will induce extra sweating which in turn cools you off more. Normally we'd assume that drinking cold beverages is best since it would provide a heat sink for excess heat produced in your body. I got interested in the NPR piece because using a different line of reasoning you can find a reasonable argument leading to a direct contradiction of the 'obvious' benefits of cold drinks.

So which is better: hot or cold drinks? The best way to determine anything is find which side the experimental evidence supports. Things get muddled, however, when you try to decide what it is you are actually measuring. This study tried cooling volunteers before exercise and found some benefit. In another study volunteer cyclists were fed hot, warm, and cold water. The difference in their heart rate and body temperature was almost identical, as expected. We do not want our core temperature to be easily manipulated; this would be bad.

For instance, an earlier article discussed by Alex employed slushies, which once consumed by some Australian athletes 'lowered the athlete's body temperature by one degree Celsius'. This in itself is intriguing; I once participated in a study in which I wore a cold suit while exercising on a bike. The orchestrators of this study defined lowering the bodies' temperature by 1.0 C equivalent to experiencing hypothermia. Yes, if these Aussies were indeed consuming enough ice to lower their core body T this much they'd have been in pretty bad shape and certainly not ready to set any personal bests (I felt pretty crummy biking while experiencing that shivering cold sensation; some people even fainted during this test). I call bullshit on the Aussie study, though it seems the original links from Alex's entry are dead. Seems they crawled back from whence they came.

I am getting slightly off track. I meant to clarify things, so here's the question (to which I will then address succinctly): how much energy is consumed converting ice to ice cold water, cold water to body-temperature water, and evaporation of that same water? Let's assume the amount of water/ice consumed is 1,000 grams, or 1 kg.

Here's where some thermodynamics comes in play. The energy required to convert one 1 kg of ice to 1kg of (ice cold) water is

Hmelt = 334 kJ.

The heat capacity if water is 4.18 kJ/kg*K. Hence the energy required to raise 1kg of ice-cold water to 37 degrees Celsius (normal body temperature) is

H = mCT 
= (1kg)(4.18 kJ/kgK)(37K)
= 154 kJ

So you absorb twice the energy converting ice to water than cold water to body-temperature water. The combined energy is 334 + 154 = 488 kJ. But let's not forget about converting liquid water to gas, i.e. the purpose of sweating. The enthalpy of vaporization for 1 kg of water is a much higher

                                                                     Hvap = 2257 kJ

That's 4.6 times more energy dissipated than the net conversion of ice to room-temperature water. The obvious interpretation is that, thermodynamically speaking, it doesn't really matter what temperature you drink your liquids if sweating is the ultimate goal: either drink something cold and gain a temporary heat sink or drink something hot, induce a slight more sweating and lose more heat that way. Sweating dissipates much more heat than anything else so it's the only thing that really matters, and precisely why humans do well in dry heat, assuming hydration is sufficient ('sufficient' meaning enough water to maintain core body temperature).

It's hard to know exactly how much energy you expend during a bout of exercise. Yes, cycling machines give up-to-the second power expenditures, but these reflect power expended on the machine, no exactly the same as the power expended by the body. Doubly labeled water estimates metabolism, but this is for longer term energy consumption and not indicative of power. Hence there's difference between some studies and others.

What cannot be debated is the physics of water. Simple thermodynamics shows there's no question where the import step truly lies.


  1. Very interesting post Graydon! I wonder how much ice-water (slushie) would be required to lower an adult's body temperature by 1 degree? By my estimate, you would only need to lose about 300 kJ to change about 70 kg of water by 1 degree, so that's assuming we were 100% water. So that could be accomplished in the slushie scenario... That is assuming that your body doesn't produce any heat, which, of course, it does. I completely agree that the Australian study must be BS.

    I would also be interested to know how much water we actually sweat. In what kind of a timeframe could you actually lose 1 kg of water due to sweat. I would imagine it would be quite variable depending on the external temperature and humidity. Perhaps the hot water vs cold/ice water debate really depends on the external conditions. If it's hot and humid and you can't sweat very much, it would be more beneficial to drink cold water. In dry heat, maybe it's better to drink something hot? Although I really can't imagine that drinking a hot drink after exercise would actually increase your rate of sweating that significantly. It would need to increase enough to compensate for the heat gained due to the hot drink.

    1. Hey Amanda. To lower the body temperature of a 70kg individual by one degree you'd need about 600 grams of ice. I used the energy balance

      m(ice) = M(person)*C(water)/[C(ice) + C(water)*dT]

      Plus since that ice would be mixed with water too, they would have had to consume over a litre of ice/water slurry. Doable, but more importantly the body wouldn't let you keep your temperature down there, so it'd only last only a moment. How useful is it to force the body to thermoregulate just before an intense bout of exercise? You'd get cramps if you did something like that just before running. Sweating by contrast works continuously.

      Lots of variables like heat, humidity, and sweating rates in general differ per person, but somewhere in the neighbourhood of 2 hours of running in hot weather will cost you a litre of water. http://journals.lww.com/cjsportsmed/Abstract/2003/09000/Fluid_Replacement_during_Marathon_Running.7.aspx