Your bomb calorimetry of a sample of carbohydrate, fat and protein yield a heat

Question

Your bomb calorimetry of a sample of carbohydrate, fat and protein yield a heat release (enthalpy of reaction) of 1.5, 8.8 and 1.5 Kcal/g of wet weight, respectively. If a 55Kg woman has 8Kg of fat stored on her body, what would her weight be if that energy was stored as carbohydrate? If she was maintaining that weight by eating a fat-only diet of 1800Kcal/day, how much food is she eating now and how much would she have to eat on a carbohydrate-only diet?

If you can please explain it mathematically. Also an explanation to go along I would really like to understand the problem thank you.

Explanation / Answer

Energy which can be yielded by 8 kg (8000 g, 1 kg = 1000 g) of stored fat in the body= 8000 x 8.8 = 70, 400 KCal

The weight of carbohydrate to be stored to yield same amount of energy released by stored fat = 70,400/ 1.5 = 46,933.33 g = 46.933 kg

Actual body weight of woman excluding stored fat is = 55 – 8 = 47 kg

If the energy is stored in form of carbohydrate then the body weight of woman would be 47 kg + 46.933 kg = 93.93 kg

Weight of fat-only diet she is consuming now to yield 1800 Kcal/day energy per day = 1800 / 8.8 = 204. 55 g

Weight of carbohydrate-only diet to be consumed daily to yield 1800 Kcal/day energy per day = 1800 / 1.5 = 1,200 g

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