In: Chemistry
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?
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.