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 = h_A(T_s - T₀) 

where A is the body surface area (roughly 1.8 m² for an adult), Ts is the skin temperature (normally 34.2°C), T0 is the temperature of the body surroundings, and h is a heat transfer coefficient. Typical values of h for the human body are 

(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) At a family party, an elderly relative calls out to you in a loud voice, “Hey, you’re an engineer, so you know everything. Explain why I’m comfortable when the room temperature is seventy degrees, but if I get into seventy-degree water in a bathtub, I’m freezing.” He stops with a smug expression on his face and along with everyone else within earshot waits for your response. What would it be?
 

8 kJ/(m h-C) (fully clothed, slight breeze blowing) 64 kJ/(m? h.C) (nude, immersed in water) %3D h