Question

When you jog, most of the food energy you burn above your basal metabolic rate (BMR) ends up as internal energy that would raise your body temperature if it were not eliminated. The evaporation of perspiration is the primary mechanism for eliminating this energy. Determine the amount of water you lose to evaporation when running for 46 minutes at a rate that uses 400 kcal/h above your BMR. (That amount is often considered to be the "maximum fat-burning" energy output. The latent heat of vaporization of water at room temperature is 2.5 106 J/kg.) kg The metabolism of 1 gram of fat generates approximately 9.15 kcal of energy and produces approximately 1 gram of water. (The hydrogen atoms in the fat molecule are transferred to oxygen to form water.) What fraction of your need for water will be provided by fat metabolism? %

Answer 1

Answer:

• At a rate of 400 kcal/h, the excessinternal energy that must be eliminated in a half-hour run is
• Q=(400x10³ cal/hr)x (4.186J/1cal)(.5h)
• Q=8.37x10⁵ J
• 1cal = 4.186J
• The mass of water that will beevaporated by this amount of excess energy is
• m _evaporated = Q/L_v

                                      =8.37x10⁵ J/2.5x10⁶J/kg

                              =.33kg

• The mass of fat burned (and thus, the mass of water producedat a rate of 1 gram of water per gram of fat burned) is
• m _produced =(400kcal/h)(.5h)/9kcal/g fat

                          =.022kg

• so the fraction of water needs provided by burning fatis
• f=(m _produced)/(m _evaporated)
• So the fraction is f=6.6%

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