Modern Engineering Thermodynamics

724 CHAPTER 17: Thermodynamics of Biological Systems
with a known heat of combustion. They elect to use benzoic
acid, which has a known heat of combustion of 6.318 kcal/g.
The test consists of igniting a tablet of the test material inside
the bomb and measuring the temperature rise of the
surrounding water. The energy equivalent (EQ) of a bomb
calorimeter is defined to be the product of the mass of the
system multiplied by its specific heat. Then, the relation between
the heat liberated by a test sample and the measured
temperature change of the water is Q = EQðT final − T initial Þ:
a. If the change in temperature of the water was 2.905°C when
a 1.1523 g tablet of benzoic acid is tested, determine the
energy equivalent of the calorimeter.
b. Then, a 1.0825-g tablet of diet cocoa is tested and produces
a temperature change of 1.699°C. Using the results of part a,
determine the caloric energy content of the cocoa in
kilocalories per gram.
32.* Rob, a young engineer, notices that, over a long period of time, he
has added 20.0 lbm (9.07 kg) of excess body fat and decides to
lose this extra weight by dieting alone. Rob’s activities are such that
his caloric intake and energy output are identical. He normally eats
two of the following meals per day, seven days per week: one
cheeseburger, one regular fries, and one 10.0 oz cola. Also, he
consumes 2.00 MJ per day of snack food while working. How long
will it take him to lose the extra 20.0 lbm of body fat by
a. Eliminating the daily snack food only?
b. Eliminating the daily snack food plus eating only one of
these meals per day?
c. Going on a total starvation diet with no food whatsoever
being consumed?
33.* Christine, an aspiring lawyer, notices that, over the past year, she
has added 10.0 lbm (4.54 kg) of excess body fat, and she
decides to work off this extra weight by jogging each evening
after work without changing her eating habits. She works 8.00
hours per day (including weekends) with an energy expenditure
rate of 0.600 MJ/h. The time spent not working or jogging is
spent sleeping or watching television at 0.300 MJ/h. Christine
eats two of the following meals per day, seven days per week:
one baked potato with cheese, one lettuce salad with French
dressing, and one pint of skim milk, plus she consumes 1.00 MJ
per day of munchies while working. How many hours must she
jog each night for three weeks to loose the extra 10.0 pounds?
34.* Do you eat like a bird? How much birdseed would a 70.0 kg
person have to eat in a day to consume proportionally as much
birdseed as does a 0.0120 kg sedentary canary per day? Birdseed
contains 60.0% carbohydrate, 12.0% protein, 6.0% fat, and
22.0% water.
35. Jim is a college wrestler weighing 145 lbf and he decides to
wrestle in the 132 lbf weight class for the upcoming season. He
plans to start his weight-loss program early so that he can be
down to the desired weight by the first practice of the season.
To accomplish this, he restricts his food intake to 1000. Calories
per day and begins an exercise program consisting of jogging for
20.0 min a day plus 10.0 min of other daily exercises that are
equivalent to climbing 20 flights of stairs at 12.0 ft per flight.
When he is not exercising, his average energy expenditure rate is
500. Btu/h for the remainder of the 24 h day.
a. What is Jim’s total energy expenditure during his 30.0 min
workout?
b. Assuming his excess weight is all body fat, how many days
before his first wrestling practice must he start the program?
36.* The amount of body fat on an average man is 19.0% of his total
mass. Tim has a body mass of 80.0 kg and it is determined that
24.0% of his total mass is body fat. He decides to swim 0.500 h
each day until his body fat has been reduced to the average. If
his daily caloric intake and energy output are equal before he
begins swimming and he does not change his caloric input, how
many days must he swim to reach his goal?
37. Mary Anne Sorensen’s airplane crashed on a mountain in the
Yukon wilderness. Sorensen weighed 150. pounds at the time of
the crash and 110. pounds when she was rescued 50.0 days
later. Assuming that death occurs when 50.0% of her body
weight is lost, estimate Sorensen’s survival time, assuming
a. A constant weight-loss rate.
b. An exponential weight loss–time relation of the form
w = w o expð −αtÞ, where α is a constant and w o is her weight
at the time of the crash.
38.* Tamara Arendt was in the same plane crash as Mary Anne
Sorensen (see the previous problem). Tamara was trained in
mountaineering and wants to hike down the mountain to
safety. However, it will take her 27.0 d of climbing at 15.0 h per
day with 9.0 h of rest per day to reach her destination. Her food
supply consists of 11.0 MJ of candy bars, 16.2 MJ of peanuts,
and 8.30 MJ of soda. The only body tissue she is able to
consume during the climb is body fat, which is 20.0% of her
initial body weight. When her body fat has been consumed she
will die of exhaustion. If she weighs 59.0 kg at the time of the
crash, is she better off waiting to be rescued with Mary Anne or
climbing down the mountain?
39. In 1638, Galileo estimated that a tree over 300. ft tall would
collapse under its own weight. Using the modern theory,
determine the diameter of the base of such a tree.
40. What is the maximum height of a California redwood tree
whose base diameter is 10.0 ft if its weight density is 40.0 lbf/ft 3
and its elastic modulus is 1.30 × 10 6 psi?
41. Since the uncertainty in the exponent in Eqs. (17.18) and
(17.19) is ±0.0800, show that the total number of heart beats
and breaths that occur over a life span is approximately the
same for all the mammals listed in Table 17.6.
42.* In a laboratory test, a student’s resting pulse rate and lung
volume are measured and found to be 60.0 beats per minute
and 8.35 × 10 –5 m 3 , respectively. What is the student’s
body mass?
43. Compute the locomotion transport number of a 4000. lbf
automobile using 60.0 hp to move at a speed of 55.0 mph.
44.* Compute the locomotion transport number of a pedal-powered
aircraft whose total mass (including the operator) is 126 kg.
The aircraft flies at 15.0 mph when the operator is supplying
1.50 hp to the pedals.
45.* It has been proposed to design a human powered vehicle (HPV)
whose total mass (including the 70.0 kg operator) is only
95.0 kg. The vehicle would be capable of traveling at 64.0 km/h
while the operator supplies power equal to that of a person
running at 5.00 m/s. Determine the locomotion transport
number of this vehicle.
46. While Paul is driving his classic 220 hp, 3000. lbf Mustang
convertible to his thermodynamics final exam, he is stopped by
a state patrolman for traveling 95 mph in a 55 mph speed zone.
Paul’s excuse to the police officer is that he is performing a
locomotion transport number homework experiment for his
thermo class. Having heard this excuse countless times before,