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 when the skin temperature is raised by 8°C due to vigorous exercise, we can use the heat transfer equation, which states that the heat loss rate is proportional to the difference in temperature between the object and its surroundings.

The formula for the heat loss rate (q) can be expressed as:

q = A * ε * σ * ΔT

Where:
q = heat loss rate (in watts)
A = surface area of the person's skin (in square meters)
ε = radiation efficiency of the person's skin (dimensionless)
σ = Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4)
ΔT = temperature difference between the person's skin and the environment (in Kelvin)

First, let's convert the temperature difference from Celsius to Kelvin:

ΔT = (28 + 8) - 22 = 14°C = 14K

Now, we can substitute the values into the formula:

q = 2 * 0.97 * 5.67 x 10^-8 * 14

Calculating this expression gives us the heat loss rate in watts.

Note: The term A * ε represents the effective surface area for heat transfer, taking into account the radiation efficiency. The value of 0.97 indicates that 97% of the person's skin surface contributes to heat exchange.

Let me calculate that for you.