Solution Manual for Fundamentals of Renewable Energy Processes 4th Edition By Aldo Vieira da Rosa, J

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Chapter 1 Introduction Problem Solutions

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Fund. of Renewable Energy Processes

Prob. Sol. c..1

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Question c. 1 If you eat 2000 kcal in a day, what is your power intake in W, hp, eV/s, and kWh/day?

We can use the conversion table in chapter 1: 2000

kcal kcal 1day 4184 J = 2000 × × = 96.9 W day day (24)(3600) s 1 kcal 96.9 W = 96.9 W ×

(2)

J 1 eV eV × = 6.05 × 1020 s 1.602 × 10−19 J s

(3)

J 1 kWh (24)(3600) s kWh × × = 2.33 6 s 3.6 × 10 J 1 day day

(4)

96.9 W = 96.9 96.9 W = 96.9

1 hp = 0.13 hp 745.7 W

(1)

Beyond these simple unit conversions, you should try to get a feeling for these units.

Solution of Question c. 1

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Fund. of Renewable Energy Processes

Prob. Sol. c..2

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Question c. 2 Suppose you are participating in an endurance race lasting 4 hours (e.g a stage of the Tour de France) and that, being an elite cyclist, you average 300 W during the race. What is your energy output during the stage in J and in kWh? If you were to sell this energy but had to price it at 15 cent/kWh in order to be competitive with electricity available from other sources, how much money would you make in this stage from this sale?

With a power output of 300W, the energy output in 4 hours would be 4 h × 300 W = 1200 Wh = 1.2 kWh. Now, 1.2 kWh = 1.2kWh × (3.6 × 106 J/kWh) = 4.32 × 106 J

(1)

At 15 cents/kWh, the 1.2kWh would be priced at 18 cents. You immediately can see that human powered generation systems have no chance to compete with established methods. You may also gain some admiration for the contraptions that have been developed for the purpose of power generation.

Notice that the 300W is the power output and should not be confused with the ”calories burned” during this event. The rate at which energy is depleted from the body will significantly exceed the 300 W. If you measured it you could get an idea of the energy conversion efficiency for these elite athletes.

Solution of Question c. 2

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Fund. of Renewable Energy Processes

Prob. Sol. c..3

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Question c. 3 The Raramuris (Tarahumaras) are a group of indigenous people in Mexico’s Copper Canyon. Running makes part of their daily life, from childhood to old age. If a Raramuri runs 4 hours a day, estimate the extra energy intake that he or she will need because of this physical activity over the course of 30 years. Estimate the distance traveled and the fuel that would be needed to travel that distance by car. You will have to make a lot of assumptions, but this is true for most energy estimates.

Answers will vary according to your assumptions. The main objective of the question is to get you to state and justify those assumptions.

One approach, further expanded in Problem 1.20, relies on a simple rule of thumb in sport physiology: any healthy person uses about 1 kcal per kilometer per kilogram of body weight when running.

1 kcal km−1 kg−1 ≈ 4000 J km−1 kg−1

(1)

Assuming an average 70 kg person. Thus a 70 kg person will use some 280 kJ/km. You can continue from here by estimating the distance covered in 30 years running 4 hours a day. To estimate the fuel consumed by a car, you could rely on average kilometers per gallon (or miles per gallon) for a typical car.

A good final step would be to estimate the impact of some of the assumptions on the answers by varying the assumed values within their expected ranges.

You could also refine your model and assume that the person is growing up (increasing his/her weight and maybe even his/her ability to run) during the 30 year period and compare with the simplified initial approach. This last step can give you some insight in regards to transient vs time averaged estimates.

Solution of Question c. 3

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