a. 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 in watts
To calculate the heat loss rate in watts, we need to use the formula for heat transfer by radiation. The formula is:
Q = A * ε * σ * (T^4 - Te^4)
where:
Q = heat loss rate in watts
A = surface area in square meters
ε = radiation efficiency (between 0 and 1)
σ = Stefan-Boltzmann constant (approximately 5.67 * 10^-8 watts per square meter per kelvin to the fourth power)
T = skin temperature in Kelvin
Te = environment temperature in Kelvin
Let's plug in the given values:
A = 2 m^2
ε = 0.97
σ = 5.67 * 10^-8 W/m^2K^4
T = 28°C + 273.15 = 301.15 K
Te = 22°C + 273.15 = 295.15 K
Now, let's calculate the heat loss rate:
Q = 2 * 0.97 * (5.67 * 10^-8) * (301.15^4 - 295.15^4)
First, let's simplify the equation inside the parentheses:
Q = 2 * 0.97 * (5.67 * 10^-8) * (2622607831.44 - 2441810914.60)
Next, let's subtract the two values inside the parentheses:
Q = 2 * 0.97 * (5.67 * 10^-8) * 180796916.84
Now, let's multiply the remaining values:
Q = 2 * 0.97 * 1.0283408 * 10^-7
Finally, let's calculate the heat loss rate:
Q ≈ 1.994 * 10^-7 watts
Therefore, the heat loss rate is approximately 1.994 * 10^-7 watts.