Although accurately evaluating the energy balance for a person is a complex problem, a simple (but reasonably accurate) model can be developed by assuming that the person has a uniform body temperature, that heat transfer to the air is governed by a single heat transfer coefficient, and that metabolism can simply be described in terms of a change in internal energy. Under these conditions, the energy balance becomes: dT mC =-hA(T – Tair) + Ometabolizm dt where m = 70 kg is the body mass, C₂ = 1 kcal/kg/K is the body's heat capacity, and A=1.8 m² is the surface area. A) Evaluate the "comfort temperature" for a person, defined as the air temperature at which the body temperature is at steady-state. The heat transfer coefficient for the human body is 4.5 kcal/hr/m²/K, the body temperature is 37 °C, and metabolizm = 120 kcal/hr. 3) When you are ill, your body increases metabolism to help fight off the disease. How long would it take for your body temperature to reach 39 °C if your metabolism were to immediately increase by 20%? Assume that Tair is equal to the comfort temperature evaluated in A.
Although accurately evaluating the energy balance for a person is a complex problem, a simple (but reasonably accurate) model can be developed by assuming that the person has a uniform body temperature, that heat transfer to the air is governed by a single heat transfer coefficient, and that metabolism can simply be described in terms of a change in internal energy. Under these conditions, the energy balance becomes: dT mC =-hA(T – Tair) + Ometabolizm dt where m = 70 kg is the body mass, C₂ = 1 kcal/kg/K is the body's heat capacity, and A=1.8 m² is the surface area. A) Evaluate the "comfort temperature" for a person, defined as the air temperature at which the body temperature is at steady-state. The heat transfer coefficient for the human body is 4.5 kcal/hr/m²/K, the body temperature is 37 °C, and metabolizm = 120 kcal/hr. 3) When you are ill, your body increases metabolism to help fight off the disease. How long would it take for your body temperature to reach 39 °C if your metabolism were to immediately increase by 20%? Assume that Tair is equal to the comfort temperature evaluated in A.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:1) Although accurately evaluating the energy balance for a person is a complex problem, a
simple (but reasonably accurate) model can be developed by assuming that the person has
a uniform body temperature, that heat transfer to the air is governed by a single heat
transfer coefficient, and that metabolism can simply be described in terms of a change in
internal energy. Under these conditions, the energy balance becomes:
mC₂ =-hA(T-Tair)+Ometabolizm
dt
where m = 70 kg is the body mass, Cp = 1 kcal/kg/K is the body's heat capacity, and
A=1.8 m² is the surface area.
A) Evaluate the "comfort temperature" for a person, defined as the air temperature at which
the body temperature is at steady-state. The heat transfer coefficient for the human body
is 4.5 kcal/hr/m²/K, the body temperature is 37 °C, and metabolism = 120 kcal/hr.
B) When you are ill, your body increases metabolism to help fight off the disease. How long
would it take for your body temperature to reach 39 °C if your metabolism were to
immediately increase by 20%? Assume that Tair is equal to the comfort temperature
evaluated in A.
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