Modern Engineering Thermodynamics

722 CHAPTER 17: Thermodynamics of Biological Systems
where P o is the basal metabolic rate, ρ is the local fluid density, A is the cross-sectional area normal to the
direction of motion, and C D is the drag coefficient of the system.
9. The life span of mammals of mass m is
Life span of mamals ðin yearsÞ = 11:8 m 0:2
10. The death rate constant k d for living systems at an environmental temperature T (in K) is
n h io
k d
= T exp 9:62 ×
T − 330:
104 − 33:2
α 330: × T
where α is a species-specific constant.
Problems (* indicates problems in SI units)
1.* Use Eq. (17.9) to determine the membrane potentials of
hydrogen carbonate ðHCO3 − =
Þ, hydrogen phosphate ðHPO 4 Þ,
and hydrogen ðH + Þ ions listed in Table 17.2.
2.* An alien scientist from a galaxy in the star system Luepke has
been able to directly measure the electrical potential required to
transport a unit charge of divalent carbon ions from outside a
human cell into the cell and finds it to be 4.10 μV. The alien
also measures the value of the chemical potential of the carbon
ion and finds it to be 0.520 J/kgmole. Using these
measurements, determine the amount of electrochemical work
required to transport 1.00 kgmole of carbon ions across the cell
membrane.
3.* A muscle contraction is brought about by the release of
calcium ions from storage vacuoles, where the calcium
concentration is 0.700 mg/mL, into the cell’s cytoplasm, where
its concentration is 0.100 mg/mL.
a. What is the electrical potential between the vacuole and the
cytoplasm?
b. If 1.00 mg of calcium ions is released in a contraction, how
much adenosine triphosphate (ATP) must be hydrolyzed
from adenosine diphosphate (ADP) according to the reaction
ATP + water ! ADP + P + 29:3 MJ/kgmole to restore the
muscle to its initial state?
4.* Assume that an individual adult in our society requires an
energy intake of 10.0 MJ/d. Let this energy come exclusively
from eating beef that was produced with a 10.0% energy
conversion efficiency. Let the beef be fed by corn produced with
another 10.0% energy conversion efficiency, and let the corn be
produced from sunlight with a 1.00% energy conversion
efficiency. Further, let the corn be grown in a region where the
solar energy flux is 20:0 MJ/ ðm 2 .dÞ:
a. Compute the number of acres (1.000 acre = 4047 m 2 )of
land necessary to grow the corn required to feed the beef
ultimately consumed by one adult person.
b. If some 16.0 × 10 9 acres are available for cultivation on
Earth today, estimate the total population that can be
supported by this food chain.
c. If the current world population is 6.00 × 10 9 people and the
population growth rate is given by p = p o expð0:0300tÞ, where
p is the population at time t, p o is the initial population, and
t is time measured in years from the present, determine the
number of years into the future when the population
calculated in part b will be reached.
5.* Stewart has a BMR of 160. kJ/d and climbs to the 13th floor of
his office building in 4.00 min while consuming only 0.0100 kg
of carbohydrate having an energy content of 17.2 MJ/kg. The
distance between the floors is 7.60 m. What is Stewart’s energy
conversion efficiency if he does not lose any weight during the
climb? Note: Stewart must supply energy to achieve his kinetic
energy motion, but this energy is not recovered when he stops.
6. Find the energy conversion efficiency of a 2000. lbf
thoroughbred racehorse with a 120. lbf jockey and tack running
1.25 miles on a flat track in 144 s. The horse accelerates to a
constant speed at the starting gate and maintains this speed
throughout the race. During the race, the horse expends energy
at the rate of 33,000. Btu/h. Ignore any aerodynamic effects.
7.* Greg, a professional weightlifter, has the capacity to convert his
internal energy into output work at a rate of 2.70 × 10 3 J/s. If
the distance from his chest to his extended arms is 0.750 m,
how much weight can he bench press in 2.00 s? What is the
horsepower output of his arms under these conditions? Assume
his arm muscles have an energy conversion efficiency of 25.0%.
8.* During an experiment, it was found that an 80.0 kg man lost
0.260 kg of body fat having an energy content of 33.1 MJ/kg by
lifting one 50.0 kg mass from the floor to a 1.50 m high shelf
every 5.00 seconds continuously for 4.00 hours. Ignoring
respiratory and perspiration losses, determine the energy
conversion efficiency of the muscular contractions.
9.* The per capita electrical power consumption in the United States
is about 200. kW · h/d. Suppose this power is generated by
having mice run in wheels that turn electrical generators. These
mice are to be feed Swiss cheese that has a metabolizable energy
content of 15.5 MJ/kg and costs $4.00 per kilogram. If the mice
have an energy conversion efficiency of 25.0%, how much will it
cost to buy the cheese needed to feed the mice who supply the
per capita energy needs?
10.* Determine the horsepower corresponding to 1.00 MJ/h. If, in an
average 24.0 h day, your energy output is 8.40 MJ, determine
your average daily horsepower output.
11.* In 6.00 h, the heat from a guinea pig melts 0.200 kg of ice in an
adiabatic calorimeter. Assuming that the heat of fusion of ice is
335 kJ/kg, determine the average metabolic heat production rate
of the animal while it is in the calorimeter.
12.* If a person’s body has a specific heat equal to that of water and
produces 6.28 kJ per min per kilogram of body mass, what is
the rate of increase in body temperature in °C per min if the
person is suddenly made adiabatic?
13.* Rumor has it that Frankenstein’s monster was brought to life by
charging it with 1.00 kW of power for 2.00 h, after which it
operated with an efficiency of only 25.0%.