Question

chemical engineering
*An adult human being at rest produces roughly 0.40 mJ/h of thermal energy through metabolic activity. Use that fact to solve the following problems.
(a)
A college student who weighs 128 pounds put off a major assignment until the day before it was due and worked for eight hours to complete it. If she is modeled as a closed adiabatic system at constant pressure, her heat capacity and molecular weight are approximately the same as that of liquid water, and her temperature was normal when she began to work, what would her temperature have been by the time the assignment was finished?
(b)
Now model the student as an open system and assume that evaporation of perspiration (evaporative cooling) is the only mechanism for heat loss. How much weight would she have lost through evaporation if she maintained a constant body temperature?
(c)
Are either of the models in Parts a and b reasonable? Explain. What is the most likely explanation of what happened to the metabolic energy produced in her body?

Answer 1

A. We know that
q= m.c. Δt
Now q= 0.40mJ/hour * 8 hours
= 3.2 * 10^-3 J.
m = 58.05 *103 g
c = 4.18 J/g°c.
therefore, Δt= q/mc
           Δt= 0.013*10^-6
Therefore, the final temperature will be = 37 + 0.013*10^-6 °c.
Assuming normal body temperature= 37°c.
b. q= m.c. Δt
Q = 3.2 * 10^-3 J.
C = 4.18 J/g°c.
ΔT = 0 (as body temperature is constant)
Therefore, m= q/cΔt
M= 0
She wouldn’t loose any weight.
c. Both these models in parts a and b are not reasonable as the human body cannot be put in an adiabatic state because the body cannot stay in an environment where gain or loss of heat is prohibited.

(1)

If this is the case, then the process of breathing would stop as breathing too involves exchange of heat.

(2)

Also, the factors responsible for weight loss cannot only be heat loss due to perspiration as the body looses weight due to processes inside the body which requires ATP like digestion, thinking etc.

(3)

The heat loss cannot occur due to perspiration if one maintains a constant body temperature.

(4)

The metabolic energy is used up in completing physical activities like completion of assisgnments and maintaining biochemical anabolic and catabolic demands of the body for carrying out various biochemical reactions.