Evaporation of perspiration

[physics1234]

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 kcal/h above your BMR. (That amount is often considered to by the "maximum fat-burning" energy output.) The metabolism of 1 gram of fat generates approximately 9.2 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?

Well, I found that the latent heat of vaporization of water is 2.5 x 10^6 J/kg
and that I need to use the formula Q=mL but I don't know where to start.

 

[marcusl]

Well, how much total energy do you burn doing the exercise? How much fat is required to produce the energy?

Can you supply the final two steps...

BTW, you'll need the latent heat of vaporization expressed in calories rather than joules.

 

[kyle8921]

I would like to clarify a few things before providing a response. First, it is important to note that the amount of water lost through perspiration during exercise can vary depending on factors such as intensity of exercise, environmental conditions, and individual factors. Therefore, the calculation provided in the content may not be accurate for everyone.

That being said, let's assume that the given information is applicable for an average person. The first step would be to calculate the total amount of energy burned during the 30 minutes of jogging at a rate of 400 kcal/h above the BMR. This would be equivalent to 400 kcal/h x 0.5 h = 200 kcal.

Next, we can use the given information that 1 gram of fat metabolism produces approximately 1 gram of water. Therefore, the amount of fat burned during the 30 minutes of jogging would be equivalent to 200 kcal/9.2 kcal/g = 21.74 grams.

Now, to determine the amount of water lost through perspiration, we can use the formula Q = mL, where Q is the energy released during the metabolism of fat (200 kcal), m is the mass of water (in kg), and L is the latent heat of vaporization of water (2.5 x 10^6 J/kg). Rearranging the formula, we get m = Q/L.

Substituting the values, we get m = 200 kcal / (2.5 x 10^6 J/kg) = 8 x 10^-5 kg. This is equivalent to 0.08 grams of water.

Therefore, the fraction of water provided by fat metabolism would be 0.08 grams / 21.74 grams = 0.0037 or 0.37%.

This calculation shows that a very small fraction of our water needs are met through fat metabolism during exercise. It is important to note that this is a simplified calculation and does not take into account other sources of water loss, such as breathing and sweat losses from other parts of the body. Additionally, it is important to maintain proper hydration during exercise to replace the water lost through perspiration.