At body temperature the latent heat of vaporization of water is Lv = 2.26 ¡Ñ 103 kJ kg−1.

(a) A naked person with a surface area A = 1.55 m2 and a skin temperature £c = 37.3 ¢XC is in a sauna room at T = 82.0 ¢XC. The person's skin has an emissivity e = 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 ¡Ñ 103 W? in kg/hr

Although someone else may help you, I cannot answer because I cannot decipher the symbols

£c, ¢XC, ¡Ñ that you are using.

Different computers print them differently. For Jiskha purposes, it is better to write "deg" for degrees and * for "times", and ^ in front of exponents. I have no clue what
£c is supposed to represent. On my computer, it looks like a British pound symbol follewed by a c.

To find the net rate of heat absorption by the person due to radiation, we can use the Stefan-Boltzmann law. The formula is:

P = e * A * σ * (T^4 - Tc^4)

where:
P is the power absorbed by radiation,
e is the emissivity of the skin,
A is the surface area of the person,
σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4),
T is the temperature of the sauna room, and
Tc is the body temperature.

(i) Substituting the values given:
e = 0.910,
A = 1.55 m^2,
σ = 5.67 x 10^-8 W/m^2K^4,
T = 82.0°C = 355.15 K,
Tc = 37.3°C = 310.45 K

P = 0.910 * 1.55 * 5.67 x 10^-8 * (355.15^4 - 310.45^4)

Using a calculator, we can simplify the equation:

P = 0.910 * 1.55 * 5.67 x 10^-8 * (24,055,520,986,853 - 3,622,011,256,303)

P = 0.910 * 1.55 * 5.67 x 10^-8 * 20,433,509,730,550

P = 0.910 * 1.55 * 1.15875665 x 10^3

P ≈ 1,170 W

Therefore, the net rate of heat absorption by the person due to radiation is approximately 1,170 W.

(ii) To find the amount of sweat that must be evaporated to balance a net rate of heat absorption of 850 W, we can use the latent heat of vaporization of water.

The formula to calculate the amount of sweat evaporated is:

S = H / Lv

where:
S is the amount of sweat evaporated,
H is the net heat absorption rate, and
Lv is the latent heat of vaporization of water.

Substituting the values given:
H = 0.850 x 10^3 W,
Lv = 2.26 x 10^3 kJ/kg = 2.26 x 10^6 J/kg

S = (0.850 x 10^3) / (2.26 x 10^6)

S ≈ 0.376 kg

To convert this to kg/hr, we divide by the number of hours in an hour (1 hour):

S/hr = 0.376 kg/hr

Therefore, approximately 0.376 kg/hr of sweat must be evaporated to balance a net rate of heat absorption of 850 W.