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.
To calculate the heat loss rate, we need to use the formula for heat transfer through radiation. The formula is:
Q = εσA(T^4 - T_env^4)
Where:
Q is the heat loss rate,
ε is the radiation efficiency,
σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4),
A is the surface area of the skin,
T is the temperature in Kelvin,
T_env is the environmental temperature in Kelvin.
First, let's convert the temperatures from Celsius to Kelvin. We can do this by adding 273.15 to both the skin temperature and the environmental temperature:
T_skin = 28 + 273.15 = 301.15 K
T_env = 22 + 273.15 = 295.15 K
Now, let's calculate the heat loss rate when the skin temperature is raised by 8 degrees due to vigorous exercise. We'll call this new temperature T_newskin:
T_newskin = 28 + 8 = 36
Now, we can calculate the heat loss rate using the formula:
Q = εσA(T_newskin^4 - T_env^4)
Plugging in the values:
Q = 0.97 * (5.67 x 10^-8 W/m^2K^4) * 2 m^2 * ((36 + 273.15)^4 - (22 + 273.15)^4)
Now we can calculate the final answer.