Energy the body expends from raising temperature of 350 mL of Diet Soda?

Question

You drink 350 mL of diet soda that is at a temperature of 5 °C.
(a) How much energy will your body expend to raise the temperature of this liquid to body temperature (37 °C)? Assume that the density and specific heat capacity of diet soda are the same as for water.
(b) Compare the value in part (a) with the caloric content of the beverage. (The label says that it has a caloric content of 1 Calorie.) What is the net energy change in your body resulting from drinking this beverage?
(c) Carry out a comparison similar to that in part (b) for a nondiet beverage whose label indicates a caloric content of 240 Calories.

Help, pleeeease!!

Answer 1

Okay. The specific heat of water is 4.184 J/gK. Water has a density of 0.998 g/mL at standard conditions. For the sake of ease of use, I'll assume these characteristics are constant throughout the process (they probably aren't, but the difference isn't likely to be significant).

Our 350 mL of soda, then, weighs about 350 x 0.998 = 349 grams. So that means it will take 4.184 x 349 = 1461 J/K to heat it up. The temperature change is from 5 to 37 C, so that's a difference of 32 C, which is the same difference in K. So that's a total of 1461 x 32 = 46767 J altogether.

One joule is 4.18 calories, so that becomes 11188 calories, but dietary Calories (with a capital c) are actually kcal, so that's 11.2 kcal of energy that's used to heat up that soda.

If you're drinking diet soda, you get 1 kcal in but use 11.2 kcal, so you have a net energy expenditure of 10.2 kcal (I never thought of drinking soda as being like exercise before...).

A non-diet soda, on the other hand, gives you 240 kcal... of which you use 11.2, leaving you having consumed still a total of 228.8 kcal. No wonder 30% of America is obese!

Hope that helps!