For anyone trying to lose weight, this question is an exciting one! If you simply want to know if your body burns calories warming up the water, the answer is yes. But if you want to know if drinking a lot of ice water can help you lose weight, or keep weight off, this "yes" needs to be qualified with some calculations.
First of all, calories are casesensitive. There are calories and then there are Calories. Calories with a big "c" are the ones used to describe the amount of energy contained in foods. A calorie with a little "c" is defined as the amount of energy it takes to raise the temperature of 1 gram of water 1 degree Celsius.
What most people think of as a Calorie is actually a kilocalorie: It takes one Calorie to raise the temperature of 1 kilogram of water 1 degree Celsius. So when you drink a 140Calorie can of cola, you are ingesting 140,000 calories. There is no cause for alarm, because the conversion applies across the board. When you burn 100 Calories jogging a mile, you are burning 100,000 calories.
So, considering that the definition of a calorie is based on raising the temperature of water, it is safe to say that your body burns calories when it has to raise the temperature of ice water to your body temperature. And unless your urine is coming out ice cold, your body must be raising the temperature of the water. So calories are being burned.
Let's figure out exactly what you're burning when you drink a 16ounce (0.5 liter) glass of ice water:
 The temperature of ice water can be estimated at zero degrees Celsius.
 Body temperature can be estimated at 37 degrees Celsius.
 It takes 1 calorie to raise 1 gram (0.0352 ounces) of water 1 degree Celsius.
 There are 454.56 grams in 16 ounces of water.
So in the case of a 16ounce glass of ice water, your body must raise the temperature of 454.56 grams of water from zero to 37 degrees C. In doing so, your body burns 16,819 calories. But that's calories with a little "c." Your body only burns 17 Calories, and in the grand scheme of a 2,000Calorie diet, that 17 isn't very significant.
But let's say you adhere to the "eight 8ounce glasses of water a day" nutritional recommendation. In 64 ounces of water, there are 1,818.24 grams. So to warm up all that water, in the course of a day, your body burns 67,275 calories, or 67 Calories. And over time, that 67 Calories a day adds up. So, while you definitely shouldn't depend on ice water consumption to replace exercise or a healthy diet, drinking cold water instead of warm water does, in fact, burn some extra Calories!
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