Question

(A) If a 3 oz candy bar produces 200 kcal on oxidation in the body, and if this energy were convertible into work, how many candy bars would a 160 -lb man have to eat in order to climb Mt. Washington (6288 ft) from Pinkhan Notch (2032 ft) without his having to call on stored energy reserves? (B) If the oxidation of fat produces 400 kcal lb-1 , what is the lower limit of weight that a 120 -lb woman will lose in making this climb if she eats nothing en route and if all of the required energy is supplied from the oxidation of the fat reserves in the body?

Answer 1

Energy of the man at the top of mountain = mgh

m = mass of the man = 160lb 160 X 453.59 = 72574.4g = 72.57kg, g = accelration due to gravity = 9.8m/s².

h = 6288 - 2032 = 4256ft = 4256 X 0.3048 = 1297.2m

Energy of the man at the top of mountain = 72.57X 9.8 X 1297.2 = 922.55KJ

Hence candy must supply 922.55KJ of energy to the man.

3 oz or 3 X 28.35 = 85.05g supply 200Kcal or 200000 X 4.18 = 836000J = 836KJ

836KJ of energy are supplied by 85.05 g of candy

1KJ will be supplied by 85.05 / 836 = 0.102g of candy

922.55KJ of energy will be supplied by = 922.550 X 0.102 = 94.1 g of candy

94.1 = 94.1 / 28.35 = 3.32 oz

Hence the man needs 3.32 oz candy bars

(B) mass of the woman in grams = 120 X 453.59 = 54430.8g = 54.43Kg

Energy required to climb = 54.43 X 9.8 X 1297.2 = 691.9KJ

Oxidation of 1lb of fat produces 400Kcal = 400000 X 4.18 = 1672000J = 1672KJ

Or 1672KJ of energy are produced by 1lb of fat

1KJ of energy are produced by 1 / 1672 = 0.0006 lb of fat

Hence 691.9KJ of energy will be produced by 691.9 X 0.0006 = 0.415 lb

Hence the woman will lose a minimum of 0.415 lb of weight.

16 oz = 1lb