# Miracle Diet Through Physics!

I was doing some swimming today, and when I got out of the pool and dried off the first thing I did was to get some ice water to cool down a bit. Good stuff, there’s not much that’s as satisfying as cold water to a thirsty person on a hot day.

Ice water is at or about 0 degrees Celsius, and my insides have to hold themselves quite closely to the classical Fahrenheit value of 98.6, which is 37 Celsius. If my body were a perfectly insulated system with no way to generate heat internally, my body would warm the water up and the water would cool my body down until they reaches a equilibrium somewhere south of that 37 degrees. But this doesn’t happen, or we would die. The human body is not very tolerant of large changes in internal temperature. Therefore all other things being equal, the body has to crank up a little bit more metabolism to produce the heat required to heat that water up to the temperature of the rest of the body.

This immediately suggests a tempting diet plan, if not a very lucrative one: drink lots of cold water. Your body burns calories warming up the H2O, you lose weight without much effort. Plausible?

Well, there’s two possibilities depending on how determined/foolhardy you are. If you actually swallow ice, your body has to warm the ice from its negative temperature up to the melting point, add the substantial heat of fusion needed to turn the water from 0-degree ice to 0-degree liquid, and then finally raise the 0-degree liquid to 37 degrees. Swallowing ice sounds like a good way to choke to death and/or damage your esophagus and stomach so I would advise strongly against it. You could chew the ice if you like enormous dental bills after you wreck your teeth. For completeness though, we’ll do the math.

Let’s say you have a kilogram of ice. It’ll fill about a liter of space. Heating it from a freezer temperature of (say) -2 C requires 2060 J of energy (which is the specific heat of 1 kilogram of ice) times the temperature change, for a total of 4120 J per kilogram.

Now add in the heat of fusion: 333,000 J per kilogram. A big number, not bad.

Finally add in the heat required to get the water from 0 to 37 degrees, i.e., 37 degrees times 4,186 J per kilogram per degree, or 154,882 J per kilogram. The total is about 492,000 J/kg. What’s that in food calories? 118, for swallowing a 1 kg block of ice whole. Not bad, but certainly not worth the effort and risk of swallowing a tremendous amount of ice whole.

What about just drinking ice water? That cuts out the first two parts of the calculation, just leaving us with the 154,882 J per kilogram. And that’s 37 food calories.

37 food calories for a liter of ice water is not a lot, but it’s not trivial either. Done once or twice a day it could add up. More importantly if you drink sugared beverages you can replace the Coke with ice water and suddenly you’re close to having 300 fewer calories per drink switched.

So of course there’s no magic way to lose weight. But considering how easy drinking cold water is, I’d say it can’t hurt. And if you switch cold water for a 270 food calorie Coke, you’ve suddenly done yourself quite a bit of good.

1. #1 Uncle Al
June 16, 2009

There is no reason to drink it. Soaking in it is just as good (less energy for kidneys bailing water). The simple solution is to live in Minnesota six months/year. Refrigeration is free.

Washington should shortly announce the National Energy Volunteer Endeavor in which every taxpayer is required to briefly run a treadmill each day, contributing a mere 1 kW-hr of electricity/taxpayer-day into the grid, saving America. Penality for NEVER violation is \$100/day.

Run the numbers.

2. #2 Kobra
June 16, 2009

Assuming 3500 KCal = 1 lb. fat, replacing two Cokes with glasses of ice water will put you at losing 1 lb. of fat every 6 days (give or take), which is a healthy rate of weight loss. Think about it.

3. #3 Kobra
June 16, 2009

Two liters*

Sorry.

Also, 2 liters of Coke equates to roughly 820 KCal. Combine that with the 2 liters of ice water to get 894 KCal.

So if you drink 2 liters of Coca Cola per day, you could be losing as much as 1 lb. of fat every 4 days (although that might be a bit too much weight loss).

4. #4 Kobra
June 16, 2009

So if you drink 2 liters of Coca Cola per day, and you replace those with 2 liters of ice water you could be losing as much as 1 lb. of fat every 4 days (although that might be a bit too much weight loss).

I’m doing all sorts of messing up today.

5. #5 dWj
June 16, 2009

I regularly eat a couple ice cubes before leaving the house on a hot day. A few minutes later I’m liable to feel a bit cool, and I’m comfortable for 15 to 20 minutes.

6. #6 ...
June 16, 2009

7. #7 Whitecoat Tales
June 16, 2009

@Kobra

But hwo drinks 2 liters of regular cola a day? I might come close to that in diet…

When you run those numbers, it’s less about the physics, and more about cutting regular pop from your diet in massive quantities. Thats less interesting physics.

8. #8 Uncle Al
June 16, 2009

Sigh. 1 kw-hr = 860.637 Calories. The average person can sustain 150 watts of work . NEVER would be a minor morning chore, less then seven hours, to safeguard America against foreign energy terrorism.

3500 Calories reside in one pound of body fat. All Washington wants is 90 lbs of your flesh evey year. That leaves you plenty. US annual electrical generation from all sources is 4.1 TW-hrs. 100 million taxpayers doing their daily duty would generate

(10^8 taxpayers)(1000 watt-hrs/day)(365.2442 days/year)/10^12 watt-hrs/TW-hrs) = 36.52 TW-hr electricity/year.

We’d be rolling in electricity – too cheap to meter! 100% rechargeable battery cars and still, too cheap to meter! Zero fossil fuel emissions, zero nukular piles, zero fuel corn from maize pimp Archer-Daniels-Midlandand and still… too cheap to meter!

Everybody would be as skinny as an East Indian share cropper.

9. #9 Kobra
June 17, 2009

@8: How do we harvest it, though?

10. #10 Matt Springer
June 17, 2009

Cold showers? Harder to calculate exact figures for, but it just might burn off another one or two dozen calories if the water was very cold. I wouldn’t expect it to become a very popular method though.

11. #11 Kobra
June 17, 2009

So, shall we call this the hypothermia diet? 😛

12. #12 Eric Lund
June 17, 2009

@Kobra: Yes, we could call it the hypothermia diet. People who live in cold climates, such as Alaska or winter-over crews in Antarctica, have to consume more calories to maintain weight than people who live in warm climates do. A typical moderately active adult male in a moderate climate needs about 2500 calories per day. A former co-worker (since retired) who has wintered over in Antarctica reported that he averaged about 7000 calories per day over the course of that year. Similarly, if you visit Fairbanks, Alaska (I have been there several times myself), you will find that restaurant portions there are large even by American standards.

13. #13 Igor Santos
June 18, 2009

What if you eat ice WHILST taking a cold shower?
On a cold day.
With a fan on.

@Kobra, I’ll have to agree commenter 7: if you replace those two liters of pop with NOTHING you would still lose weight.

14. #14 DRK
June 18, 2009

This idea is not new; my Macroeconomics textbook back in the eighties (sorry, can’t remember its title) attributed this concept to Arthur Laffer, inventor of the Laffer curve and supply-side economics. (He took lots of cold baths in order to lose weight. The textbook described him as “the still-pudgy Arthur Laffer”). I am skeptical of ANY theory espoused by Mr. Trickledown.

Although I have to admit that he looks somewhat slimmer in recent photographs.

15. #15 Rob
June 18, 2009

Of course you could just wear less clothes (especially in winter)

And

16. #16 hedberg
June 19, 2009

Physicist Phillip Morrison studied the energy expended by bicycle racers in the Tour de France. I believe that this was presented as part of his PBS series “Ring of Truth.” He concluded that a typical bicycle racer consumed about 7000 food calories per day and that most of this energy was expended in cooling the body as opposed to accelerations and overcoming wind resistance (which, I suppose is an acceleration). That Phelps swimmer guy, it has been reported, consumes about 12,000 food calories per day when in full training. Surely a major portion of that has to be spent for temperature maintenance.

17. #17 fizzixs
June 22, 2009

an interesting calculation is always entertaining, though
there is a fallacy to the notion of ingesting so called negative calories. Attempting a program of ingesting ice or sitting in cold water, will likely induce behavior to reduce caloric expenditure or increase caloric intake.

18. #18 Pascale
August 12, 2009

My husband, an endocrinologist for adults, has seen obese patients who ingest 10 liters of sweetened soda a day! The pounds just melt off if you switch them to diet (or even half diet), regardless of the temperature.