Question

The human body generates heat by the metabolism of carbohydrates and other food materials. Metabolism provides energy for al biological activities. The metabolic process also generates heat, and there are special cells in the body whose main function is heat generation. Now let us assume that our friend Joe BlueHen ingests 1 L of ice, which he allows to melt in his mouth before swallowing.

a) How much energy is required to melt the ice and warm the water to the body temperature?

b) If 1 g of fat when metabolized releases approximately 42 kJ of energy, how much fat will Joe burn by ingesting the water?

c) Suppose that instead of ice, Joe drank 1 L of water at 0 degrees Celsius. How would the answers to parts a and b change?

Answer 1

a) Ice density is= 0.9167g/cm3

1L=1000cm3 which means that 1L of ice is equivalent to 916.7g of ice or 0.9167kg.

Ice fusion latent heat is =334*10^3 J/Kg, so the energy needed to pass 1L of ice to water would be

Ei->w=0.9167*334*10^3= 306KJ

Then the amount of energy needed to warm the water from 0°C to 37°C (body temperture) is

DeltaE=Cvw(Tf-Ti)

Cvw=water specific heat=4180 J/(kg K); tf= final temperature=37°C= 310K; ti= initial temperature=0°=273K

Delta E=4180(310-273)=155KJ/Kg

this multiplied by the water/ice mass= 0.9167kg. would be the amount of energy necessary to warm the water to 37°C

Delta E=155*0.9167=142KJ

Total Energy necessary=306KJ+142KJ= 448KJ.

B)Simply dividing Total Energy by 42KJ/g of fat...

Total fat= 448/42=10.6g

C) in this case the energy necessary to melt the ice isn't considered, so the total energy would be only equal to the amount of energy needed to warm the water from 0°C to 37°. Also the density of the water differ from the ice, water density is 1Kg/L.

Total energy= 4180KJ/Kg(310-273)*1Kg= 155KJ

Total grams of fat= 155/42=3.69g