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Energy Consumption

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Energy Consumption1890 1910 1930 1950 197

01990

Traditional Energy

Use Per Person (kW)

.35 .30 .28 .27 .27 .28

Industrial Energy

Use Per Person (kW)

.32 .64 .85 1.03 2.04 2.52

Total World Energy

(Terawatts (1012W)

1.0 1.5 2.3 3.3 8.4 16.8

World Population

(Billions (109))

1.5 1.7 2.0 2.5 3.6 6.0

(16.8 1012W ~ 2.1 108 barrels of oil day-1)

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Energy flow in environment

~1.7x1013 Watts

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Limits on Energy EfficiencyEngines which burn a fuel or use a heat source to do work or provide energy are called “heat engines” and have maximum efficiency of

where the temperature of the heat source is TH and the heat sink is TC.

The fuel in power stations usual heats steam turbines to ~ 3000C, hence

(K) T

(K) T - 1 = )( EfficiencyH

c

% 48 = 372 + 300

372 + 20 - 1 efficiency maximum

Thus using electricity to provide heating is grossly inefficient.

In combined heat and power systems, such as the one in this university, electricity is generated locally and the heat is also used.

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By far the largest potentialsource of renewable energy.

Problems of solar power: (i) Diffuse i.e. low intensity.(ii) Variable over the day, season, and region (iii) Intermittent because of cloud cover. (iv) Lowest intensity in the coldest regions with the largest energy consumption per person.

BUT High intensities in most populous regions of the Earth.  To meet current world energy consumption require the use of an area of 500 500km of the Sahara at 20% conversion efficiency.

Solar power

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Flat Plate CollectionThe commonest forms of solar energy converters are simply ‘flat plate’ collectors which are often used for heating water.

Very poor for driving engines or producing electricity as the temperatures are low.

Consider a system that heats water to 60oC and uses this to power a heat engine with a cold sink at 20oC

12% = 60 + 273

20 + 273 1

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Concentration of solar energy

Use fixed reflectors or systems that track the sun (heliostats).

Pump oil through pipes at the focus of such mirrors. Temperatures of 200oC can be achieved. Efficiency then ~ 40%.

Small-scale solar stoves and large scale solar furnaces based on focused sunlight can also be constructed.

Systems designed for energy production concentrate the sunlight.

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Biomass (Wood Burning etc.)

Wood burning has been the most important fuel has historically.

Still produces about 10% of all the energy used globally.

Growing trees for fuel is inefficient in terms of labour and land use.

Crops such as sugar beet and cane can the be used to produce fuels such as alcohol.

Burning such fuels or burning wood does not add to the net amount of CO2 in the atmosphere as the carbon in the plants was removed from the atmosphere while the plants grew.

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Solar Cells (Photovoltaics)

Solar cells directly convert solar energy into electrical power.

The first solar cells, produced in the mid-fifties, had conversion efficiencies of ~ 5%. Efficiencies of >> 20% have been achieved in silicon solar cells and >> 30% in other semiconductors.

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Wind power

Wind energy is derived from solar energy.

Windmills have been used for grinding grain and pumping water for at least 3,000 years and for the production of electricity for the last 100 years.

The total energy contained in the winds around the earth greatly exceeds the total human energy consumption.

Recently there has been considerable commercial interest in wind power.

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Energy in WindFor a wind turbine of area A and efficiency , a wind velocity and a density of air r power produced

P = ½Av3 Watts

The efficiency of a wind turbine has an upper limit of 59%. The best commercial wind turbines achieve about 40% efficiency.

The v3 dependence of the power makes the choice of sites for wind turbines very important.

At 5ms-1 Power is 75Wm-2. At 10ms-1 it is 600Wm-2 (standard temperature and pressure ).

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Total Available Wind Energy

To produce large amounts of energy one would need to construct large-scale wind farms.

These are arrays of wind turbines, separated by distances large enough to stop the wind speed at a given turbine being significantly reduced by the presence of other the other turbines.

Would need to cover ~5% of the Earth's surface with such wind farms to meet the current total world energy consumption of 1.7 1013 Watts.

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Variations of Wind Speed

Wind speed is variable over both long and short time periods.  

Fluctuations in wind speed give very large power fluctuations. Wind turbines have to withstand large rapidly varying forces.

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Water turbines: Micro-Hydroelectric plants

Can use the kinetic energy of streams and rivers.

Water powered mills were once extremely common.

The available power is exactly the same as for a wind turbine i.e. ½ρAv3 where A is the area of the turbine.

But density of water is 103 kg m-3 i.e. ~ 1000 times greater than air.

For v=3ms-1 and A=1m2 the available power is 13.5kW.

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Hydroelectric Power

H

Water inx m s-1

Water outx m s-1

Hydroelectric power uses the potential energy of the falling water.

It is an energy source of world importance meeting about 6 % of world energy consumption.

Dam height H meters, water density ρ.

Energy that could be extracted per m3 of water is ρgH.

If reservoir fed by rivers at a rate of x m3s-1 available power is xρgH.

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Wave Power

The water in a wave moves in a circular manner. For deep water waves, unaffected by the ocean bed, volume elements of the water move in circles of radius

where z is the average depth below the surface and k is the wavevector (=2π/λ).

[kz]A = A(z) o exp

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Available PowerDeep water waves: ω2 = gk, g is the acceleration due to gravity.

The waves move with a velocity v=dω/dk= g/2ω.

A volume element of mass m has energy ½ mω2A2.

A layer of thickness dz will have an energy of ½ρω2A2dz per m2.So the energy per unit area of the ocean surface is

The available power per unit width is

where T is the period. Note that the available power is proportional to the square of the wave amplitude and to the wave period, T.

Jm 4

gA =

4kA =[2kz]dz A = E 2-

2o

2o

22o

2-o

exp

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Wm 16

TAg =

8Ag

= Power 1-2o

22o

2

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Wave Power Utilisation:

Floating rocking devices: e.g. `Salter Ducks' Land based air columns: Typically 10 100 kW

devices.

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Tidal power: Origin of the TidesThe Earth and Moon rotate about their common centre of gravity.

At the centre of mass the Earth the gravitational attraction between the Earth and the moon precisely provides the centripetal acceleration.

At 2 the gravitational attraction is greater than is needed to provide the centripetal acceleration, at 3 it is less.

The water at the surface will tend to move outwards at both points.

The Earth rotates within this bulged envelope of water.

Moon

2

3

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Earth and Moon rotate about their common center of mass

l

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Tidal period

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Earth maintains its orientation in space with respect to the stars during the

moons rotation

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Animation: Earth-moon rotation

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Spring and Neap Tides The gravitational attraction of the sun also gives rise to tides.

The maximum tidal amplitude (Spring tides) occur when these effects are additive (Earth/Sun/Moon in line).

The minimum amplitudes (Neap tides) occur when they subtract (Earth and Moon at 90o with respect to earth).

Moon

Sun

MoonSun

Spring (Maximum) Tide Neap (Minimum) Tide

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Spring and Neap Tides

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Tidal BarrageTrap incoming tidal waters and use the water’s potential energy.

Assume barrage width, W, at a point on the coast where the tidal range (twice the amplitude) is R. At high tide it encloses an area WL of water.

Total stored energy is therefore

It is possible, in principle, to extract this much energy every tidal period T. So the available power is

3

gAR = dxx

R

WgL = dE =E

22R

oRo

Watts3T

gARP

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Water in and out

R

L

W

The potential energy of a layer of water thickness dx is dE=mgx=(ρWydx)gx where ρ is the water density and y =xL/R.

y

x

X=0