When you jog, most of the food energy you burn above your...

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 $400 \mathrm{keal} / \mathrm{h}$ above your BMR. (That amount is often considered to be the "maximum fatburming" energy output.) The metabolism of 1 gram of fat generates approximately $9.0 \mathrm{kcal}$ 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? (The latent heat of vaporization of water at room temperature is $2.5 \times 10^{6} \mathrm{~J} / \mathrm{kg} .$ )

Key Concepts

Fat Metabolism and Energy Yield

Fat metabolism refers to the biochemical processes that break down fat molecules to release energy. This process not only produces energy but also yields water as a byproduct. The efficiency of fat oxidation—quantified as the energy released per unit mass of fat oxidized—affects both the energy available for bodily functions and the incidental production of metabolic water.

Latent Heat of Vaporization

The latent heat of vaporization is the amount of energy needed to change a unit mass of a substance from liquid to gas at constant temperature. In the context of thermoregulation, this property of water is crucial because it determines how much energy can be eliminated through sweating, thereby cooling the body while causing water loss.

Unit Conversion in Energy Calculations

Many problems in physiology and biochemistry require accurate conversion between different units of energy, such as converting between kilocalories and joules. Proper unit conversion is essential for quantifying energy flows in metabolic processes and matching the energy required for physical processes like the evaporation of sweat.

Energy Expenditure Beyond Basal Metabolic Rate

This concept involves the energy used during physical activities that exceeds the energy required for maintaining basic physiological functions at rest. When a person exercises, they burn additional calories that must be dissipated to prevent overheating, which brings into focus the body’s need to manage extra thermal energy through mechanisms like sweating.

Evaporative Cooling and Heat Dissipation

Evaporative cooling is the process by which the body loses heat through the evaporation of sweat. The energy used in exercise is converted to internal energy, and evaporation is an effective method to remove this excess energy, as it takes a significant amount of energy—quantified by the latent heat of vaporization—to convert liquid water into vapor.

Transcript

0:00 Hi there.

00:01 So for this problem, we are told that when you jog, most of the food energy you burn above your basal metabolic rate ends up as internal energy that will raise in your body's temperature if you were not eliminated.

00:15 So for this problem, we need to determine the amount of water that you lose to evaporate the to evaporation when you're ruining 30 minutes at a rate that uses 400 kilo calories per hour above your basal metabolic rate so the metabolism of one gram of fat generates approximately so one gram of fat generates 9 kilo calories so of energy and produces approximately 1 gram of water.

01:14 So we also need to determine what fraction of your need for water will be provided by fat metabolism.

01:28 And we are also given the latin heat of vaporization of water at room temperature.

01:34 So with that information, the first thing that we are going to obtain is the heat.

01:41 So at a rate that is given the access internal energy that must be eliminated in half an hour run is the following is.

01:51 The heat is equal to 400 times 10 to the 3 calories per hour.

02:02 And we multiplied this by a factor of conversion to pass from calories to joules.

02:08 So we multiply this by 4 ,186 joules divided by 1 ,186 jules, divided by one calorie.

02:19 And this times the hour that we know is half an hour because it is 30 minutes, so it's going to be 0 .5 hours.

02:29 So from this, we obtain a value of 8 .37 times 10 to the 5 joules.

02:39 So the mass of water that will be evaporated by this amount of assets energy is going to be the following.

02:48 The mass of evaporation, evaporation, or evaporated, is going to be equal to the heat that we obtain divided by the latin heat...

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