# During a period of relative inactivity, the average rate of transport of enthalpy by the metabolic anddigestive waste products leaving the body, minus the rate of enthalpy transport by the raw materialsingested and breathed into the body, is approximately AH -300 kJ/h. Heat is transferred from the bodyto its surroundings at a rate given by:Q = hA(T To)where A is the body surface area (approximately 1.8m2 for an adult), Ts is the skin temperature (normally34.2°C), To is the temperature of the body surroundings, and h is the heat transfer coefficient. Typicalvalues of h for the human body are:(fully clothed, slight breeze blowing)h 8 kJ/(m2-h-°C)=h 64 kJ/(m2-h-°C)(in a bathing suit, immersed in water)a)Consider the human body as a continuous system at steady state. Write an energy balance on thebody, making all appropriate simplifications and substitutions.b) Calculate the surrounding temperature for which the energy balance is satisfied (i.e. when acold) for a clothed person and for a person swimming. You canperson would feel neither hot norassume skin temperature remains constant

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Step 1

Given information in the problem as follow:

Average rate of transport enthalpy by metabolic and digestive waste products leaving the body – the rate of enthalpy transport by raw material ingested and breathed into the body = -300 KJ/h

ΔH = -300 KJ/h

Rate of heat transferred from the body to its surroundings, Q = h A (TS-TO)

TS (Skin Temperature) = 34.2⁰C

TO = Surrounding Temperature

Surface area of body = 1.8 m2

h = 8 kJ / (hr∙m2∙⁰C)        (Fully clothed, slight breeze blowing)

h = 64 kJ / (hr∙m2∙⁰C)      (In a bathing suit, immersed in water)

Step 2

(a)

Assumption: Human body as a continuous system at steady state

Energy balance equation for the human body:

Step 3

(b)

Now to calculate the surrounding temperature for two different situ...

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