Energy for our activities is provided by the chemical energy of the foods we eat. The absolute value of the rate of conversion of this chemical energy into other forms of energy (ΔE/Δt) is called the metabolic rate. The metabolic rate depends on many factors - a person's weight, physical activity, the efficiency of bodily processes, and the fat-muscle ratio. The table lists the metabolic rates of people under several different conditions and in several different units of measure: 1 kcal = 1000 calories = 4186 J. Dieticians call a kcal simply a Cal. A piece of bread provides about 70 kcal of metabolic energy.
Table. Energy usage rate during various activities.
Type of activity ΔE/Δt (watts) ΔE/Δt (kcal/h) ΔE/Δt (kcal/day)
45-kg person at rest 80 70 1600
68-kg person at rest 100 90 2100
90-kg person at rest 120 110 2600
68-kg person walking 3 mph 280 240 5800
68-kg person moderate exercise 470 400 10000
68-kg person heavy exercise 700 600 14000
In 1 hour of heavy exercise, a 68-kg person metabolizes 600 kcal - 90 kcal = 510 kcal more energy than when at rest. Typically, reducing kilocalorie intake by 3500 kcal (either by burning it in exercise or not consuming it in the first place) results in a loss of 0.45 kg of body mass (the mass is lost through exhaling carbon dioxide - the product of metabolism).
Part A
A 68-kg person wishes to lose 9.0 kg in 3 months. Estimate the time that this person should spend in moderate exercise each day to achieve this goal (without altering her food consumption).