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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Asked Oct 6, 2019
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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 AH -300 kJ/h. Heat is transferred from the body
to 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 (normally
34.2°C), To is the temperature of the body surroundings, and h is the heat transfer coefficient. Typical
values 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 the
body, making all appropriate simplifications and substitutions.
b) Calculate the surrounding temperature for which the energy balance is satisfied (i.e. when a
cold) for a clothed person and for a person swimming. You can
person would feel neither hot nor
assume skin temperature remains constant
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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 AH -300 kJ/h. Heat is transferred from the body to 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 (normally 34.2°C), To is the temperature of the body surroundings, and h is the heat transfer coefficient. Typical values 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 the body, making all appropriate simplifications and substitutions. b) Calculate the surrounding temperature for which the energy balance is satisfied (i.e. when a cold) for a clothed person and for a person swimming. You can person would feel neither hot nor assume skin temperature remains constant

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Expert Answer

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:

Rate of enthalpy tranported into body - Rate of enthalpy tranported out from body
-Rate of enthalpy accumulation inside the body-Rate of enthalpy consumed inside
the body +Rate of enthalpy generation inside the body =0
300-Q-0-0+0 = 0
Q =300kJhr
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Rate of enthalpy tranported into body - Rate of enthalpy tranported out from body -Rate of enthalpy accumulation inside the body-Rate of enthalpy consumed inside the body +Rate of enthalpy generation inside the body =0 300-Q-0-0+0 = 0 Q =300kJhr

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Step 3

(b)

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

Q 300kJ/hr
0-hA(T, —То)
hА(T, — Т.) %—300
8x1.8x(34.2-Т.) — 300
300
34.2 - Т
8 x1.8
34.2 -Т, 3 20.83
Т. 3 34.2 — 20.83
Т, 313.37' С
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Q 300kJ/hr 0-hA(T, —То) hА(T, — Т.) %—300 8x1.8x(34.2-Т.) — 300 300 34.2 - Т 8 x1.8 34.2 -Т, 3 20.83 Т. 3 34.2 — 20.83 Т, 313.37' С

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