Exponential Growth

Our energy dilemma can be analyzed in terms of fundamental principles. A corollary of the first law of thermodynamics is: it is a physical impossibility to have continued exponential growth of any product or exponential consumption of any resource in a finite system.

The present rate of consumption and the size of the system give a tendency for people to perceive the resource as either infinite or finite. The total energy output of the sun and the amount of mass in the solar system are infinite sources at our present rates of energy and material use, even though the solar system is finite. Even just the amount of solar energy received by the earth is a very large resource. The energy dilemma is defined within the context of the system, and our present energy dilemma is due to the finite amount of fossil fuels on the earth.

An easy way to understand exponential growth (Figure 2.1) is to use the example of money. Suppose Sheri receives a beginning salary of $1/year with the stipulation that the salary is doubled every year, a 100% growth rate. It is easy to calculate the salary by year (Table 2.1). After 30 years, her salary is $1,000 million per year. Notice that for any year, the amount needed for the next year is equal to the total sum for all the previous years plus 1.

Suppose a small growth rate is used, the doubling time (T2) can be estimated by

where R = % growth per unit time, generally years. Doubling times for some different yearly rates are given in Table 2.2.

FIGURE 2.1 Exponential growth with a growth rate of 100% per year.

TABLE 2.1

Salary at Growth Rate of 100% Per Year

TABLE 2.1

Salary at Growth Rate of 100% Per Year

Year

Salary, $

Amount = 2'

Cumulative,

0

1

20

1

1

2

21

3

2

4

22

7

3

8

23

15

4

16

24

31

5

32

25

63

6

64

26

127

7

128

27

255

8

256

28

511

t

2t

2t+1 - 1

30

1 * 109

230

Doubling Times for Different Rates of Growth

TABLE 2.2

Doubling Times for Different Rates of Growth

Growth,

Doubling Time,

%/year

years

1

69

2

35

3

23

4

17

5

14

6

12

7

10

8

9

9

8

10

7

15

o EP

1000 Year

2000

FIGURE 2.2 World population, year 0 to 2005.

There are numerous historical examples of growth: population, 2-3%/year; gasoline consumption, 3%/year; world production of oil, 5-7%/year; electrical consumption, 7%/year. Notice that if we plotted the value per year for smaller rates of growth, the curve would be the same as Figure 2.1, only the time scale along the bottom would be different (Figure 2.2). The projection of the growth of population in the future (Figure 2.3) assumes the growth rate will decrease to 0.5% in 2050. The United Nations projects a leveling off at 9 * 109 to 11 * 109 people by the year 2200.

However, even with smaller rates of growth, the final result is still the same. When consumption grows exponentially, enormous resources do not last very long. Order of magnitude calculations make the analysis quite clear.

FIGURE 2.3 World population, 1900 to 2050, with United Nations projections for 2010 to 2050, under median variant.
Solar Panel Basics

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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