Question

If you drink cold water, it will soon warm up to body temperature (about 37 C) This takes energy. Therefore, you ought to be able to keep your weight down even if you eat fattening food provided you also drink lots of cold water, right?Estimate what volume of cold water you would need to drink to overcome the effect of eating one chocolate sundae. (A chocolate sundae contains about 500 Cal. Recall that 1 Cal, the "calorie" normally used in the US to measure the energy content of food, is 1000 cal, or 1kcal.)

Answer 1

18.4 L

Step-by-step explanation:

A chocolate sundae contains 500 Cal. Considering that 1 Cal = 1 kcal and 1 kcal = 4.184 kJ, a chocolate sundae contains:

500 Cal × (4.184 kJ / 1 Cal) = 2.09 × 10³ kJ

Let's suppose we drink water at 10°C that increases its temperature to 37°C by absorbing this heat (Q). We can find the mass of water using the following expression.

Q = c × m × ΔT

where,

c: specific heat capacity of the water

m: mass

ΔT: change in the temperature

Q = c × m × ΔT

2.09 × 10³ kJ = (4.19 kJ/kg.°C) × m × (37°C - 10°C)

m = 18.4 kg

Considering the density of water to be of 1 kg/L, the volume of water is 18.4L.