During a period of relative inactivity, the average rate of transport of enthalpy by the metabolic and digestive waste products leaving the body minus the rate of enthalpy transport by the raw materials ingested and breathed into the body is approximately ΔH = —300 kJ/h. Heat is transferred from the body to its surroundings at a rate given by Q = hA (T_s — T₀) where A is the body surface area (roughly 1.8 m² for an adult), T is the skin temperature (normally 34.2°C), 7’0 is the temperature of the body surroundings, and h is a heat transfer coefficient. Typical values of h for the human body are h = 8 kJ/(m² ∙ h ∙ ˚C) (fully clothed, slight breeze blowing) h = 64 kJ/(m² ∙ h∙ ˚C) (nude, immersed in water) (Data taken from R. C. Seagrave, Biomedical Applications of Heat and Mass Transfer, Iowa State University Press. Ames, Iowa, 1971.)

(a) Consider the human body as a continuous system at steady state. Write an energy balance on the body, making all appropriate simplifications and substitutions.

(b) Calculate the surrounding temperature for which the energy balance is satisfied (i.e.. at which a person would feel neither hot nor cold) for a clothed person and for a nude person immersed in water.

(c) In terms of the preceding discussion, suggest why you feel colder on a windy day than on a day where the temperature is the same but there is no wind.