Lecture IV

Physics 367

Consumption of Electrical Energy


Electricity is one of the most common forms of energy we encounter.

The past century is characterized by:

immense expansion in our use of energy
huge increases in the size of our generating plants

Notable periods:

The 60's largest growth period in the century.
The 70's two energy crises.

Year

Rate of Electrical Consumption Growth

Population Growth

19617.2% 1.6%
19627.0%  
19636.9%  
19646.7%  
19656.0%  
19665.6%  
19675.5%  
19685.6%  
19695.5%  
19709.3%  




Predictions

So how are predictions made? What will happen with energy demand in the next century?

Consider the tables below of Actual Energy Use and Predictions in earlier years, where 1kWh = 3.6x106J; 1 Quad(Btu)= 0.293TkWh.

U.S. Energy Use (TkWhe)

YearActual Use
195010.1
196013.2
197019.9
198023.0
199024.7
199928.3

Projections of U.S. Energy Use in 2000 (TkWhe)
Year Source Projection
1972 D.C. Chapman et al. 24-123
1972 A. Lovins 36.8
1972 Sierra CLub 41.2
1973 J.C. Fisher 39.0
1974 W. Hafele 47.0
1976 A. Lovins 22.1
1976 F. von Hippel 25.0-26.2
1978 National Academy of Sciences 19.7-25.3
1979 Department of Energy 35.9
1979 Exxon Corp. 25.0
1981 Edison Electric Institute 34.5
1981 Department of Energy 30.0
1981 Mellon Institute 25.9
1991 Department of Energy 29.3

There are many different ways to estimate or project future behavior.

Steady State.....
Linear Projections.....
Exponential Projections.....

Projections can NOT be made in a vacuum!

Steady state and linear projections:

are not applicable when the growth depends on the initial size.
may be applicable locally

Example: exponential or geometric growth

Population....if the cockroach doubling time is 1 week then how many cockroaches will there be after 10 weeks?

Let N0 be the initial population. Then

after 1 week 2N0 = 21N0
after 2 weeks      4N0 = 22N0
after 3 weeks      8N0 = 23N0
after n weeks              = 2nN0

Let t0 be the doubling time then we can write:

N = N0 2t/t0

Notice this has the form:

N = N0 2bt

where b=1/t0

Other equivalent forms include:

N = N0 10at

and

N = N0 ect

where: 1/a is the time to increase the population by a factor of 10

     1/b is the time to increase the population by a factor of 2.
     1/c is the time to increase the population by a factor of e = 2.713.

Projections on the demand for electricity certainly depend on the population so we would expect a geometric growth.

Actual predictions depend on many factors:

Price
Profit
Ease of extraction
Return on investment
Damage
War

In many cases a Logistic Curve is more applicable than an exponential curve

See Figure 5.8

Example:Combustion of Fossil Fuel

Fossil fuel contains carbon, and it is burned by combining with oxygen in the air. Air is about 20% oxygen and 80% nitrogen. The combustion converts chemical energy stored in the fuel to kinetic energy [thermal energy]. Since fossil fuels contain hydrogen in addition to carbon, combustion also produces water.

There are several problems with burning:

fuels contain other chemical compounds for example, sulfur.
sulfur can cause acid rain.
nitrogen may combine with oxygen producing nitrogen oxides.
nitrogen oxides can cause acid rain.

 burning is more a complex process than indicated by

fossil fuel + oxygen carbon dioxide + water + energy.

A more accurate characterization is:

fossil fuel + oxygen + nitrogen
carbon dioxide + water + energy
+ sulfur oxides
+ nitrogen oxides
+ particles.

Consider a typical coal-fired power plant:

a plant generating 1000 MW of electricity

Power is the amount of energy used in a certain time divided by the time (Watt = 1J/s).

Our coal plant generates 1 billion watts of power--a billion joules of energy per second. It does this by burning coal. The coal is carried by automatic machines [endless belts] from the coal pile in the coal yard.

The plant burns about

100 kilograms of coal per second,

and produces

15 kilograms of ash per second,
5 kilograms of sulfur dioxide per second,
and
300 kilograms of flue gases per second.

Just think about those numbers!

Problem of the day

OSU has a constant undergraduate enrollment of 42,000 students. No students flunk out or transfer in from other colleges and so the residence time of each student is 4 years. How many students graduate each year?

This is a steady state problem commonly called a box problem.

Let:  M = number of students at any given time

   T = the residence time of each student

In this example the ratio of the stock in the box (M students) to the flow rate (in [Fin] or out [Fout]) (entrance or graduation rate) is called the residence time.

Thus if Fin is the rate of inflow to the box and Fout is the rate of outflow, the steady state condition is:

Fin = Fout

and

M/Fin = M/Fout = T

Solution:

What do we know?

The stock, M, is 42,000
The residence time, T, is 4 years
The graduation rate, Fout is unknown.

so:

M/Fout = T

or

Fout = M/T

Fout = (42,000 students)/(4 yrs)

Fout = 10,500 students/yr