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Modern Engineering Thermodynamics

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Problems 725<br />

the officer asks Paul for the value of his experimental LTN,<br />

promising to release him if his answer is correct. Paul replies,<br />

“0.29, sir.” The officer then consults the state patrolman’s guide<br />

to locomotion transport numbers for the correct value. Does<br />

Paul get arrested?<br />

47.* Tom is a 75.0 kg bicyclist who recently averaged 42.0 km/h<br />

during a 240. km race with an 8.40 kg racing bike. If he<br />

consumes 4100. L of oxygen and has a muscle energy<br />

conversion efficiency of 25.0%, determine<br />

a. His rate of conversion of oxygen in L/min.<br />

b. His locomotion transport number.<br />

48. Sharla, weighing 140. lbf, absorbs 0.500 hp in her muscles<br />

while pedaling a 7.00 lbf bicycle at 25.0 mph into a 5.00 mph<br />

head wind in air at 70.0°F. Her frontal cross-section is 4.00 ft by<br />

2.00 ft, and her drag coefficient is 0.500.<br />

a. Compute her locomotion transport number.<br />

b. Determine her most efficient velocity on the bicycle.<br />

49.* Jim has a frontal cross-section of 2.00 m high by 0.500 m wide<br />

and can run at 4.00 m/s and swim at 1.00 m/s. His drag<br />

coefficients in air and water are 1.30 and 1.10, respectively.<br />

What speeds should Jim run and swim at to be most efficient?<br />

Assume Jim’s BMR is 0.300 MJ/h.<br />

50.* Determine which of the following expends the most energy over<br />

a 20.0 mi course:<br />

a. A 126 kg pedal-powered aircraft flying at a speed of<br />

15.0 mph with a locomotion transport number of 0.134.<br />

b. A fast walking 75.0 kg person walking at a speed of<br />

2.50 mph,<br />

c. Determine the energy expenditure rates of the person<br />

powering the aircraft and the person walking and comment<br />

on the feasibility of maintaining these rates over the 20.0 mi<br />

course.<br />

51. If King Kong was ten times bigger than a normal human being,<br />

a. Find his locomotion transport number while riding a bicycle<br />

(assume his bicycle locomotion transport number is 25.0%<br />

of the minimum value shown on Figure 17.12).<br />

b. What was his most efficient walking velocity (assume the<br />

same drag coefficient as for a human).<br />

52. Convert the k d /α information associated with Eq. (17.33) from<br />

metric units into <strong>Engineering</strong> English units.<br />

53.* If a cold-blooded animal has an activation entropy of death of<br />

3088 kJ/(kgmole · K) at 25.0°C, what is the change in k d /α for<br />

the animal if it moves to an environment at 20.0°C?<br />

54.* If the specific molar activation enthalpy of death is 800. MJ/<br />

kgmole, the compensation temperature is 330. K, and the<br />

constant β = −276 kJ/ðkgmole.KÞ, determine the specific molar<br />

activation entropy of death.<br />

Design Problems<br />

The following are open-ended design problems. The objective is to<br />

carryoutapreliminarydesignasindicated. A detailed design with<br />

working drawings is not required unless otherwise specified by your<br />

instructor. These problems have no specific answers, so each student’s<br />

design is unique.<br />

55. Design an inexpensive apparatus that measures the energy<br />

conversion efficiency of an in vivo human arm or leg muscle.<br />

Measure the oxygen consumption rate of the test subject to<br />

determine the energy input rate. Include proper transducer<br />

instrumentation for the necessary input data, and specify<br />

adequate output electronics. Provide assembly and detailed<br />

drawings sufficient to allow a technician to fabricate, assemble,<br />

and test your design.<br />

56. One of the problems with the commercially available bomb<br />

calorimeters is that they can test only small samples on the<br />

order of a few grams. Design a bomb calorimeter large enough<br />

to burn a sample as large as 1 pound. Pay special attention to<br />

safety considerations in your design. Do not attempt to<br />

construct or test your design.<br />

57. Design a system that measures the rate of metabolic<br />

heat production of a small warm-blooded animal. You may<br />

use either a direct or an indirect calorimetry technique.<br />

Provide engineering drawings and instrumentation<br />

specifications.<br />

58. Design a whole body calorimeter that measures the<br />

instantaneous metabolic heat loss rate from an entire human<br />

body. Your system must be large enough or else sufficiently<br />

mobile that measurements can be made while the test<br />

subject is doing physical labor without restraint from your<br />

system.<br />

59. Design a variable resistance rowing exercise machine that has a<br />

direct digital readout of the instantaneous energy expenditure<br />

rate of the user. This means you have to specify or design<br />

transducers that measure the instantaneous work rate (i.e.,<br />

power) done on the machine. This power can be absorbed by<br />

the machine either electrically or mechanically. Provide<br />

assembly and detail drawings of your design plus specify all the<br />

electronics necessary to process the transducer signals and<br />

provide the proper digital output.<br />

60. Design an apparatus that measures the metabolic heat loss rate<br />

and surface temperature of a yeast culture or a small insect at<br />

various environmental temperatures. Construct and calibrate this<br />

apparatus if possible, and make enough measurements to plot<br />

_Q /T b for some living system vs. time at various environmental<br />

temperatures. Does _Q /T b increase or decrease as the<br />

environmental temperature decreases?<br />

Computer Problems<br />

The following open-ended computer problems are designed to be<br />

done on a personal computer using a spreadsheet, equation solver,<br />

or programming language.<br />

61. Develop an interactive computer program that returns the user’s<br />

basal metabolic rate, oxygen uptake rate, carbon dioxide<br />

production rate, pulse rate, and breathing rate when the user<br />

inputs his or her mass or weight.<br />

62. Develop an interactive computer program that outputs<br />

the energy conversion efficiency of a person or an animal.<br />

The user must be prompted for input data regarding work<br />

performed, energy output resulting in increases in potential<br />

or kinetic energies, and changes in body total internal<br />

energy. You may assume that the specific internal energy of<br />

the body is constant for activities that occur over short time<br />

periods.<br />

63. Develop an interactive computer program that provides the user<br />

with the metabolizable energy content of foods chosen from a<br />

menu. Allow the user to specify the desired energy units<br />

(Calories, Btu, MJ) of the output.

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