   Chapter 11, Problem 36P

Chapter
Section
Textbook Problem

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 30. minutes at a rate that uses 4.00 × 102 kcal/h above your BMR. (That amount is often considered to be the “maximum fat-burning” energy output.) The metabolism of 1.0 grams of fat generates approximately 9.0 kcal of energy and produces approximately 1.0 grams 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? (The latent heat of vaporization of water at room temperature is 2.5 × 106J/kg.).

To determine
The fraction of water provided by fat mechanism.

Explanation

Section 1:

To determine: The excess internal energy.

Solution: The excess internal energy is 837kJ .

Explanation:

Given Info: Running time 30 min, rate is 4.00×102kcal/h .

Formula to calculate excess internal energy in 30 min of run is,

Qexcess=Rt

• Qexcess is the excess internal energy,
• R is the rate of elimination,
• t is the time of running,

Substitute (4.00×102kcal/h) for R and 30 min for t to find Qexcess .

Qexcess=(4.00×102kcalh)(4186J1kcal)(30min)(0.016667hr1min)=837kJ

Thus, the excess internal energy is 837kJ .

Section 2:

To determine: The mass of water that will be evaporated by the excess internal energy.

Solution: The mass of water that will be evaporated by the excess internal energy.

is 0.33kg .

Explanation:

Given Info: Running time 30 min, rate is 4.00×102kcal/h , and latent heat of vaporization is 2.5×106J/kg

Formula to calculate the mass of water that will be evaporated by the excess internal energy is,

mevap=QexcessLv

• mevap is the mass of water evaporated,
• Lv is the latent heat of vaporization of water at room temp,

Substitute 837kJ for Qexcess and 2.5×106J/kg for Lv to find mevap

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