# How much more energy does it take for a human body to heat 0C ice vs 0C water?

I'm trying to determine if going through the trouble of ingesting ice is worth the hassle versus ingesting ice-cold water, but my physics skills are rusty.

If I drink a gram of ice water at ~0C, my body has to heat the water to 37C.

Per wikipedia, the water will be heated by

$$1\text{ g} \times \underbrace{37\text{ K}}_\text{Temperature difference} \times \underbrace{ 4.1813 \frac{\text{J}}{\text{g K}}}_\text{Specific heat of water} = 155\text{ J}$$

Whereas if I ingest a gram of ice, in addition to those 155 Joules, it will need to heat by 334 Joules to do the transformation from ice to liquid. So the payoff to ingesting ice instead of water is about 3 times more calories burned.

Is my reasoning sound?

Note: You could turn my question into a meta-question by attacking the logic of ingesting cold water for burning calories, but please be so kind as to keep your answers to the physics question I've stated.

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Hi Ross, and welcome to Physics Stack Exchange! This is actually not a bad physics question at all. Since it's a physics site, we're not going to care about the logic of drinking cold water to burn calories - that's part of the weird world of biology ;-) In fact if you had asked whether drinking cold water burns calories we'd probably come up with a model just like what you have here. –  David Z Jan 2 '12 at 22:30
You'd have to ingest 1.7kg of ice to burn off the energy of one average donut. –  Nick Bedford Jan 3 '12 at 2:48
Which is better than $$1.7 \times 3.15 = 5.35 kg$$ of 0C water :-) It also explains why I'm not in the TGIF donut club. It may be quackery, but thanks for the physics analysis. :-) –  Ross Rogers Jan 3 '12 at 3:21
It'd be interesting to see how eating ice compares to not wearing a sweater on a cold day in terms of calories burned. –  shujaa Jan 3 '12 at 22:30
I believe part of the biological response is hormonal and unrelated to the specific energy transfer, so the actual thermic shock is important to seeing a hormonal response. See [1] and [2]. Anyways, giving it the old college try to see what happens. Pro'lly wont kill me. –  Ross Rogers Jan 3 '12 at 23:06
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I think $334$ joules is not right, you should calculate the energy of a gram of ice to melt/become water at 0C than add energy that you have calculated above. Please find the latent energy of melting. If you calculate correctly, you need much bigger energy to swallow a gr of ice until it becomes water at $37^o \text{C}$ in your body.