A person with skin area 2 m2 and 0.97 radiation efficiency is at rest and has a skin temperature of 28 C in an environment with a uniform temperature of 22 C.
Calculate the heat loss rate if the skin temperature is raised by 8 C by vigorous exercise.
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To calculate the heat loss rate when the skin temperature is raised by 8°C due to vigorous exercise, we need to use the equation for heat loss through radiation.
The equation for heat loss through radiation is given by:
Q = ε * A * σ * (T^4 - T_0^4)
where:
Q = heat loss rate
ε = radiation efficiency of the object (given as 0.97)
A = surface area of the skin (given as 2 m^2)
σ = Stefan-Boltzmann constant (5.67 × 10^-8 W/(m^2·K^4))
T = final skin temperature (28°C + 8°C = 36°C)
T_0 = ambient temperature (22°C)
Now let's plug in the values:
Q = 0.97 * 2 * 5.67 × 10^-8 * (36^4 - 22^4)
Calculating the values inside the parentheses:
Q = 0.97 * 2 * 5.67 × 10^-8 * (1,726,146 - 331,776)
Simplifying further:
Q = 0.97 * 2 * 5.67 × 10^-8 * 1,394,370
Q = 0.000110 * 1,394,370
Calculating the multiplication:
Q ≈ 153.38 W
Therefore, the heat loss rate when the skin temperature is raised by 8°C due to vigorous exercise is approximately 153.38 Watts.