Final answer:
The rate of heat transfer to you by radiation in a sauna can be calculated using the Stefan-Boltzmann law. By plugging in the given values into the equation, the rate of heat transfer can be determined to be 113 W.
Step-by-step explanation:
The rate of heat transfer to you by radiation in a sauna can be calculated using the Stefan-Boltzmann law. According to this law, the rate of heat transfer by radiation is proportional to the emissivity of the object, its temperature, and the fourth power of the absolute temperature of the surrounding environment. The equation is given by:
Q = εσA(T₁⁴ - T₂⁴)
where:
Q is the rate of heat transfer by radiation
ε is the emissivity of the object
σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m²K⁴)
A is the surface area of the object
T₁ is the skin temperature
T₂ is the ambient temperature
Plugging in the given values:
Q = (0.98)(5.67 x 10^-8 W/m²K⁴)(1.50 m²)((37.0 + 273.15)⁴ - (50.0 + 273.15)⁴)
Calculating this equation will give you the rate of heat transfer by radiation to you in the sauna. The correct option among the given choices is a) 113 W.