Sweating is one of the main mechanisms with which the body dissipates heat. Sweat evaporates with a latent heat of 2430 kJ/kg at body temperature, and the body can produce as much as 1.3 kg of sweat per hour. If sweating were the only heat dissipation mechanism, what would be the maximum sustainable metabolic rate, in watts, if 83% of the energy used by the body goes into waste heat?
Answer should be in W
Let P be the maximum metabolic rate.
0.83 P is concerted into body heat
0.83 P = 1.3 kg/hr*(1/3600 hr/s)*2430*10^3 J/kg
Solve for P, in J/s (Watts)
I get about a kilowatt
1057.2
To find the maximum sustainable metabolic rate, we need to determine the total energy dissipated through sweating.
Total energy dissipated through sweating per hour can be calculated using the following formula:
Energy dissipated = mass of sweat produced per hour * latent heat of sweat evaporation
Given:
Latent heat of sweat evaporation = 2430 kJ/kg
Maximum sweat produced per hour = 1.3 kg
Converting kJ to J: 1 kJ = 1000 J
Energy dissipated = 1.3 kg * 2430 kJ/kg * 1000 J/kJ = 3,159,000 J/h
Now, since 83% of the energy used by the body goes into waste heat, we can calculate the sustainable metabolic rate:
Sustainable metabolic rate = Energy dissipated / 0.83
Sustainable metabolic rate = 3,159,000 J/h / 0.83 ≈ 3,805,421 J/h
Converting from J/h to W:
1 W = 1 J/s
Sustainable metabolic rate = 3,805,421 J/h / 3600 s/h ≈ 1057 W
Therefore, the maximum sustainable metabolic rate, if sweating were the only heat dissipation mechanism and 83% of the energy used by the body goes into waste heat, would be approximately 1057 watts.
To find the maximum sustainable metabolic rate, we need to calculate the amount of heat that can be dissipated through sweating and convert it to watts. Here's how:
Step 1: Calculate the amount of heat dissipated through sweating:
- We know that sweat evaporates with a latent heat of 2430 kJ/kg at body temperature.
- The body can produce as much as 1.3 kg of sweat per hour.
- So, the total heat dissipated through sweating in an hour would be: 2430 kJ/kg * 1.3 kg = 3159 kJ.
Step 2: Convert the heat dissipated to watts:
- Convert kilojoules to joules by multiplying by 1000: 3159 kJ * 1000 = 3,159,000 J.
- Divide by the time in seconds to get the rate in watts. Since there are 3600 seconds in an hour, the rate would be: 3,159,000 J / 3600 s = 877.5 W.
Step 3: Calculate the maximum sustainable metabolic rate:
- Based on the given information, 83% of the energy used by the body goes into waste heat.
- So, the maximum sustainable metabolic rate would be: 877.5 W / 0.83 = 1057.83 W (rounded to two decimal places).
Therefore, the maximum sustainable metabolic rate, if sweating were the only heat dissipation mechanism, would be approximately 1057.83 watts.