A naked person with a surface area of 1.55 meters squared and a skin temperature of 37.3 degrees is in a sauna room at T = 82.0 degrees. The person's skin has an emissivity of 0.910. She evaporates sweat from her body to balance the rate of heat absorption by radiation.

(i) Neglecting any heat production due to metabolism, what is the net rate of heat absorption by the person due to radiation? in W
(ii) How much sweat must be evaporated per hour to balance a net rate of heat absorption of H = 0.850 × 103 W? in kg/hr

Radiation power absorbed

= Area*sigma*emissivity*(T2^4 - T1^4)
T1 and T2 are the skin and sauna wall temperatures, respectively, in Kelvin.
sigma is the Stefan-Boltzmann constant. (Look it up).

ii) Divide the heat absorption rate (W or J/s) by the heat of vaporization of water, 2.26*10^6 J/kg. Then convert kg/s to kg/hr

To determine the net rate of heat absorbed by the person due to radiation and the amount of sweat that must be evaporated per hour to balance the heat absorption, we can use the Stefan-Boltzmann law and the heat of vaporization of sweat.

(i) The net rate of heat absorption by the person due to radiation can be calculated using the following formula:

Net heat absorption = emissivity * Stefan-Boltzmann constant * surface area * (T^4 - Ts^4)

where:
- emissivity is the emissivity of the person's skin (given as 0.910)
- Stefan-Boltzmann constant is a physical constant (approximately 5.67 x 10^-8 W/m^2K^4)
- surface area is the surface area of the person's body (given as 1.55 m^2)
- T is the temperature of the sauna room (given as 82.0 degrees Celsius, which needs to be converted to kelvin by adding 273.15)
- Ts is the skin temperature of the person (given as 37.3 degrees Celsius, which also needs to be converted to kelvin)

Let's calculate the net rate of heat absorption by substituting the given values into the formula:

Net heat absorption = 0.910 * 5.67 x 10^-8 * 1.55 * (355.15^4 - 310.45^4)

(ii) To determine the amount of sweat that must be evaporated per hour to balance the net rate of heat absorption, we can use the heat of vaporization of sweat. The heat of vaporization is the amount of energy required to convert 1 kg of water from liquid to vapor at a constant temperature and pressure.

Given that the net rate of heat absorption is H = 0.850 × 10^3 W, and the heat of vaporization of sweat (Hv) is typically around 2454 kJ/kg (which needs to be converted to watts by dividing by 3600), we can use the following relationship:

Heat absorbed by evaporation = sweat evaporation rate * heat of vaporization

Solving for the sweat evaporation rate, we get:

Sweat evaporation rate = Heat absorbed by evaporation / Heat of vaporization

Substituting the given values into the formula, we can calculate the sweat evaporation rate:

Sweat evaporation rate = (0.850 × 10^3) / (2454 kJ/kg / 3600)

Now, let's calculate both the net rate of heat absorption by radiation (i) and the sweat evaporation rate (ii).