introduction to energy and thermodynamics v4...

ES 181 v. 4 An Introduction to Energy and Thermodynamics

H.A. Stone, G. H. McKinley, M.J. Aziz

This course (ES 181) provides a detailed introduction to Engineering Thermodynamics (often called “Classical Thermodynamics”) with a passing mention to concepts of kinetic theory and statistical mechanics (often referred to as “Thermal Physics”). More detailed studies of the latter subject are covered in the course Physics 181. Outline of this document:

1. Introductory Remarks and Definitions 2. Energy Sources and Interconversion 3. Global and U.S. Energy Usage 4. Examples of Energy Interconversion Devices.

1. Introductory Remarks and Definitions A) A good place to begin is by trying to define the science we wish to study: therme = Greek for “heat” dynamis = Greek for “force” Thermodynamics is the science that deals with ‘heat’ and ‘work’ plus the material properties of substances which bear a relation to heat and work. • heat and work are two different forms of energy (another concept which is very common but

hard to explain; try defining ENERGY = ??? ) We can start with a very restricted definition, from Newtonian Mechanics: Work is defined as product of a (force acting on a body)×(distance body moves under action of that force). By coupling ideas from •THERMODYNAMICS • SOLID MECHANICS • HEAT AND MASS • FLUID MECHANICS TRANSFER it is possible to analyze quantitatively a wide range of practical engineering applications. Indeed the ideas behind thermodynamics are important not only in engineering but also in physics, chemistry and biology; although the approaches may be different, concepts remain the same. This course attempts to unify many of these ideas. Thermodynamics provides a conceptual and mathematical framework for describing the energy content and energy flow in physical systems. The mathematics required is relatively straightforward (integration and partial derivatives), far more important (and difficult to achieve) is a clear and complete physical and conceptual understanding of the systems described by these laws.

ES 181 An Introduction to Energy and Thermodynamics

2

B) An Overview of the Importance of Thermodynamics: Engineering

Sciences

Energy content of a system. equivalence of work & heat and their INTERCHANGE

Rate of process Classical

Thermo-dynamics

•chemical•mechanical•aeronautical

•civil•environmental

•materials

⎫⎪⎪⎪⎪⎬⎪⎪⎪⎪⎭

• fluid mech. • heat and mass

transfer

Biology Energy cycles

• muscles • respiration • photosynthesis

Reaction pathwaysEnvironmental response

Food chain

•⎧⎪•⎨⎪ •⎩

• water and air cycles

Thermo dynamics

Physical Chemistry

• chemical reactions and molecular synthesis

Kinetic Theory

Materials Science

colloid scienceformation and material

properties of compounds,mixtures and substances

•⎧⎪ •⎪⎨⎪⎪⎩

• phase equilibria

(gases, liquids, solids) + their interchanges

• materials processing; manufacturing

—interfaces and interfacial properties

Statistical Thermo-dynamics

Physics — based on a molecular level description

e.g. Lasers, transistors, microelectronics

— prediction of materials properties

— statistical mechanics — quantum mechanics

(quantized nature of internal energy)


3

"Not knowing the second law of thermodynamics is like never having read Shakespeare"C. P. Snow (Author of a famed essay entitled “The Two Cultures” on the

similarities and differences between the fields of science and the liberal arts, and those who practice them)

"A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore, the deep impression which classical thermodynamics made upon me. It is the only physical theory concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown."

Albert Einstein, Autobiographical Notes

C) ENERGY —”The ability to do work” or "the ability to exert an action on surroundings" As we have already mentioned, energy can occur in many different forms. • Kinetic Energy 21

2 mv • Potential Energy mgh (gravitational field) 21

2 kx (spring)

• Chemical Energy ∆H released during phase change or breaking/formation of chemical bonds

• Solar Energy hν We wish to understand and quantify the physical mechanisms governing the interchange of energy. We do this through a fundamental set of “Laws of Thermodynamics” • commonly known as the “zeroth law, first law, second law, third law...of thermodynamics” We are used to using different units for each of these terms e.g. • electrical energy Kilowatt-hours • atoms & electrons electron Volts (eV) these are all different • heat Joules (J), kilojoules (kJ) measures of energy • food calories (cal.), (kilo)Calories (Cal.) • engineering Btu (British thermal unit) This diverse range of commonly-employed units is a recognition of the fact that the study of energy in various forms is important in all fields of Physics, Chemistry, Engineering and Biology and that it developed independently in each science during the 17th, 18th, and 19th centuries. The recognition of the “equivalence of heat and work” or in other words the interconversion of energy from one form to another did not come to completion until the work of James Joule (1818-1889)


4

As part of this course, we must become adept at understanding this interchange both physically and mathematically by being able to readily convert units from one form to another: 1 Btu = 1055 J = 778.2 ft-lb = 252 cal. 1 kW-h = 3.61 x 106 J = 3413 Btu 1 electron Volt (eV) = 1.602 × 10-19 J. The first place to look when you need interconversion factors is in Table A.1 of your textbook (Sonntag) but the conversion factor for the electron Volt (above) and the handout "Fundamental Physical Constants" are available for quick reference and supplementary information, respectively. A scale of important energies. Various quantities of energy of human significance are indicated on the scale in Joules. A log scale is used because we need to cover almost 50 orders of magnitude! From M. Goldstein and I.F. Goldstein, The Refrigerator and the Universe (Harvard University Press, 1993) �-4

-6

-8

-10

-12

-14

-16

-18

-20

-22

14

12

10

8

6

4

2

0

-2

-4

32

30

28

26

24

22

20

18

16

14

10

10

10

10

10

10

10

10

10

10

�10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

10

1 erg

�Fission of U(235)�atom

Energy of H2��Photon of green light1 electron volt

Kinetic energy of �mercury atom �at 500K

Energy output per day� of 100 MW power plant

1 kiloton nuclear fission bomb

Coal (per ton)

Crude oil (barrel)

U.S. Daily energy use per capita

Daily average human calorie need1 Kwh

2000 kg car at 75 km/hr

Thermal energy,�1 Kg mercury at 500 K

1 BTU

1 calorie

1 joule

Energy radiated by �sun in 1 second

Estimated world fossil�fuel reserves

�

U.S. annual energy�consumption

1 Quad (1015 BTU)

Solar energy intercepted�by Earth in 1 second �(clear day)

�


5

2. Energy Sources and Interconversion A. Solar Energy The sun is the source from which almost all energy consumed on earth is derived. The

interconversion of this energy into a number different forms is known as the energy cycle Two small additional sources of energy are : • geothermal power • tidal power

solar energy Geothermal heat released from the interior (radioactive processes) Tidal power generated by the moon’s (and sun’s) gravitational pull. (Rot. KE → GPE and KE of tides)

It is the solar energy provided by the sun that heats air and water and thus drives the wind

and water cycles. This initial energy "input" is responsible for rainfall and other precipitation that reaches the ground, flows into rivers (can provide hydroelectric power if moving water turns a turbine) and thus back to the ocean and other large bodies of water;

Of course, solar energy also provides the energy source for photosynthesis. • Short time scale: plant life → source of food for animal life. • Long time scale: formation of fossil fuels peat → lignite → subbituminous → bituminous → anthracite

(sequence of stages in conversion of plant matter to coal; each stage differs in carbon and moisture content).

Some modern uses of solar energy: •solar thermal electric generators — solar collectors responsible for heating a fluid that may either be used as a heat source, or to drive a turbine. • photovoltaics — direct conversion of solar energy to electric energy.


6

B. Thermodynamics and the food chain.

• The entire agricultural cycle is dependent on the interchange and transformation of various forms of energy.

• The term ‘bioenergetics’ is concerned with the transformation of energy in living systems

(beginning at the level of cells). • The term ‘biomass’ commonly refers to the combustion (or reaction) of biological

material to generate energy; e.g. wood, alcohol fuels, methane... The overall cycle has the following schematic form:

CO2+H2O CO2+H2O ⇓ ⇑ radiant → chlorophyll → synthesis of large molecules; → oxidation by cells → work (solar) typically carbohydrates and other foods ↓ energy (chemical energy) the conversion of chemical energy to:

photosynthesis bygreen plants

()

respirationoxidationof food

by animals

mechanical work: muscle contraction chemical work: growth

electrical work: e.g., eel light: firefly


7

C. An Example of Energy Interconversion When we turn on a light switch, the light emitted has a long history of interconversion. There are many different possible pathways but three common ones are: Solar Energy Radiation 6000°C at surface

reflected = 39% UV absor. = 10%

photosynth. = 0.1% remainder = thermal motion of atmosphere

Chemical Energy Photosynthesis by plants

Water Cycle (evaporation

condensation)

not Chemical energy but Thermal Energy of molecules

“Potential” Energy stored chemically

Coal, oil, LNG reserves

Energy Storage • reservoirs • dams

Potential Energy storage through Gravity

• Input of substantial Mechanical Energy and Thermal Energy “Heat and Beat”

refinery/mining Kinetic energy

→ Mech. Energy

Thermal → Mechanical energy

steam turbine generator

Radioactive decay, producing heat

Electrical energy electric generator power distribution grid Thermal energy (heat and light)

light switch

Light re-radiation of energy

1: fossil fuel

2: hydro-electric

3: nuclear


8

Other sources of“alternative energy generation”: solar energy • photovoltaics All different forms wind energy of “potential tidal energy energy” sources biomass nuclear energy • fission

⎧⎪⎪⎪⎨⎪⎪⎪⎩

• fusion D. Thermodynamic Efficiency The efficiency of an energy conversion process can be defined as:

efficiency (η) =Useful energy or work output

total energy input or energy converted ×100%

As we shall see, the second law of Thermodynamics requires that any process in which energy is converted from one form to another or in which useful work is extracted can never be 100 %. The remainder of this ‘lost energy’ goes towards the increase of a quantity known as ‘entropy’. To achieve a better understanding of entropy it is useful to turn to a detailed microscopic or statistical mechanical analysis of matter, but entropy can usefully be thought of as a measure of the ‘degree of disorder’ or randomness of the substance. Example: Thermodynamic efficiency of some common energy conversion devices Device Energy Conversion Path Efficiency

Electric Generators (mechanical→electrical) 70 - 99% Electric Motor (electrical →mechanical) 50 - 90% Gas furnace (chemical →thermal) 70-95% Fossil Fuel Power Plant (chemical →thermal →mech. →electrical) 30 - 40% Nuclear Power Plant (nuclear →thermal →mechanical →electrical) 30 - 35% Automobile Engine (chemical →thermal →mechanical) 20 - 30% Fluorescent lamp (electrical →light) 20% Incandescent lamp (electrical →light) 5% Solar cell (light →electricity) 2 - 25% Fuel cell (chemical →electricity) 60 - 95% •A large part of engineering thermodynamics is understanding the sources of inefficiency in different energy conversion devices, why they arise, and how to minimize them.


9

•If we have a multi-step process, then the overall thermodynamic efficiency is equal to the product of the individual efficiencies. For example if we re-consider what happens when we idly flip on a light switch, the light emitted has a long history of interconversion: from the table above, the overall thermodynamic efficiency for the conversion of chemical energy into light is η = 0.35 × 0.90 × 0.05 = 1.6% !! E). Other Important Thermodynamic/Economic considerations: • The concept of energy density is becoming increasingly important. i.e. what is the number of Joules available/unit mass of source material storing energy?

e.g. • why don't we see cars running on coal-fired engines? •the total energy available from a given mass of lead-acid or nickel-hydride or Li+

ion battery is a limiting step in electric car development, portable computer evolution....

• Another idea of growing importance is “scaleability” of a power source

i.e. how easy is it to double the total power output of a given source simply by doubling the elements of the engineering design?

• moderately scaleable: combustion engines, fossil fuel power plants • highly scaleable: fuel cells, photovoltaics, windmills, tidal power generators


10

3. Global and U.S. Energy Usage References; •DOE website (Annual Energy Review): http://www.eia.doe.gov/aer •DOE webiste (International Energy Annual): http://www.eia.doe.gov/iea •2001 Intergovernment Panel on climate change, http://www.ipcc.ch/ In 2004 the U.S. total energy consumption was 99.7 × 1015 Btu (99.7 Quads) which is a consumption rate of 105.2 × 109 GJ/yr or 3.3 TW (3.3 × 1012 watts) or 47.1 MBPD (millions of barrels of oil/ day). This corresponds to a power consumption rate of approx 11.4 kW on a per capita basis! In 2004 the world total power consumption was 15 TW (you can use the info provided above to convert to other units), or 2.34 kW on a per capita basis. Projected future power consumption depends on many variables but could double by the year 2050 (Source: http://nsl.caltech.edu/energy.html):

A. Global usage of various fuel sources (2003 Data): Coal Natural

gas Petroleum Nuclear Hydroelectric

Power (HEP) Wood, Geothermal, Solar, Wind

U.S. % 22.7 23.5 39.7 8.1 2.9 3.3@ World % 23.9 23.5 38.5 6.3* 6.5 0.9@ *NB France generates about 38% of the power it consumes from atomic fission reactors. This accounts for 80% of the power France produces; the rest is imported. @ -- The energy in this column is approximate, as wood consumption is approximate.


11

•The U.S. accounts for (296 x 106/6.45 x 109) = 4.6% of global population but approximately 22% of total energy consumption. •China accounts for about (1.31 x 109/6.45 x 109) = 20.3% of the population but about 10.8% of the total energy consumption. •U.S. Production of oil peaked in 1970 and world oil production is predicted to peak circa 2005, followed by the skyrocketing of prices for petroleum products and a suddenly-rediscovered incentive to develop alternative sources for 40% of our energy. See Hubbert's Peak handout.

B. Impact of energy use on global climate change 86% of global energy use comes from the burning of fossil fuels, which releases into the atmosphere CO2, the most important so-called "greenhouse gas". The amount released per unit energy generated (the "carbon intensity") varies according to the energy source:

Energy Source (from www.eia.doe .gov/oiaf/1605/coefficients.htm

Coal Wood Petroleum Natural Gas

Renewables

Pounds CO2 per million BTU 215 195 160 117 0 Atmospheric levels of greenhouse gases correlate strongly with global temperatures as shown in the plot below that spans 400,000 years.

Left: Temperature and atmospheric concentrations of greenhouse gases CO2 and CH4 derived from air trapped within ice cores taken from ice cores in Antartica. Right: Atmospheric CO2 levels have varied from 260 to 290 ppm over the history of human civilization. From 2001 Intergovernment Panel on climate change. Left: http://www.grida.no/climate/ipcc_tar/wg1/pdf/TAR-02.PDF Right: http://www.grida.no/climate/ipcc_tar/wg1/pdf/WG1_TAR-FRONT.PDF

Dots: world oil production through the year 2000. Upper and lower dashed curves are projections assuming the ultimate discoverable oil is 1.8 trillion barrels (area under lower curve) or 2.1 trillion barrels (upper curve). From K.S. Deffeyes, Hubbert's Peak: the Impending World Oil Shortage (Princeton University Press, 2001).


12

Atmospheric CO2 levels have varied from 260 to 290 ppm over the history of human civilization. Due to a century of fossil fuel burning, atmospheric CO2 levels are now above 370 ppm and rising, causing global warming.

Past millennium and projected century of (left) CO2 and (right) temperature. Differing scenarios reflect differing assumptions about future human activity, e.g. how soon we will start to significantly reduce CO2 emissions. From 2001 Intergovernment Panel on climate change, http://www.ipcc.ch/ (http://www.ipcc.ch/pub/un/syreng/spm.pdf)

Among the "robust findings" (expected to be relatively unaffected by uncertainties) of the intergovernmental panel on climate change(http://www.ipcc.ch/pub/un/syreng/spm.pdf): Nearly all land areas are very likely to warm more than the global average. More energy in the atmosphere will lead to more intense and more frequent storms. Increased summer drying and the associated risk of drought is likely over most mid-latitude continental interiors. Projected climate change will have both beneficial and adverse effects on both environmental and socio-economic systems, but the larger the changes and the rate of change in climate, the more the adverse effects predominate. The adverse impacts are expected to fall disproportionately upon developing countries and the poor persons within countries. Agricultural productivity would decrease in most regions of the world for warming beyond a few °C.

After CO2 emissions are reduced and atmospheric concentrations stabilize, surface air temperature continues to rise slowly for a century or more. Thermal expansion of the ocean continues long after emissions have been reduced, and melting if ice sheets continues to contribute to sea-level rise for many centuries. From 2001 Intergovernment Panel on climate change, http://www.ipcc.ch/ (http://www.ipcc.ch/pub/un/syreng/spm.pdf)


13

We are starting to run out of oil, but there is plenty of coal and plenty of effort at replacing oil with coal (e.g., coal liquefaction). Coal, however, has an even greater carbon intensity than oil. Any technological solution we implement (e.g. massive investments in efficiency improvements and wind, nuclear, and photovoltaic power generation) will take decades to build on a big enough scale to have an impact on the global energy balance. The lowest level at which we can stabilize the atmospheric CO2 concentration is already unprecedentedly high and goes up with each year of inaction. No single technological solution is evident, and scientific and engineering efforts on just about all seriously-considered technological solutions are likely to be of great value. C. Energy Efficiency Energy consumption is directly related to the economic performance of a country as seen in the plot on the right. For many rapidly developing countries, energy availability is becoming a key constraint affecting economic growth (e.g. India, China, SE Asia) US Energy Efficiency

Year GNP ($bn in Chained 2000

Dollars)

Energy Consumption

(109 Btu)

Btu/($GNP) Oil Energy Consumption

(109 Btu)

Btu/($GNP)

1970 3,798 67,143 17.68 29,537 7.78 1990 7,155 82,080 11.47 33,550 4.69 2000 9,856 98,960 10.04 38,404 3.90 2004 10,806 99,740 9.23 40,130 3.71

Left: Energy and GNP vs. time, from http://www.eia.doe.gov/oiaf/aeo/demand.html. Right: Comparison of energy use per capita vs. GNP per capita for various countries. (The World Bank, “World Development Report”, 1987).


14

D. Electrical Power Generation and Consumption in the USA In 2004, the USA generated 14.2 quads of useful electricity (about 0.5 TW) from 40.77 quads (about 1.4 TW) of raw fuel sources, which is an efficiency of 34.8 %. Transmission losses and conversion inefficiencies account for the rest! Electricity Flow, 2004 (Quadrillion Btu): http://www.eia.doe.gov/emeu/aer/diagram5.html

Sources (left) and uses (right) of US electricity: Left: http://www.eia.doe.gov/cneaf/electricity/epa/figes2.html Right: http://www.eia.doe.gov/neic/brochure/elecinfocard.html


15

E. The overall picture of US energy use Source: (2003)

Coal Natural gas

Petroleum Nuclear Hydroelectric Power (HEP)

Wood, Geothermal, Solar, Wind

U.S. % 22.7 23.5 39.7 8.1 2.9 3.3@ Usage, by sector (U.S. 2004): Residential+Commercial 38.8% • Electricity, light, heating, air conditioning

• Schools, offices, stores

Industrial 33.3% • Manufacturing Transportation 27.9% •trains, planes, automobiles, subways Economic Impact Policy (national and international) •energy cost affects market cost • development and support of energy infrastructures •health risks • promote cogeneration, more efficient uses of waste heat •tax incentives/fines for use/abuse • R&D for new energy sources or more efficient processes of energy, raw materials and for current energy producing/consuming systems environmental awareness • 1970 Clean Air Act (first Federal policy)


16

Energy Sources

Environmental Impact

oil natural gas coal

• Air pollution (particulate emissions); Soil, water pollution (formed from combustion)

nuclear hydroelectric geothermal

• CO2 increases in the atmosphere • Coupled to global temperature & climate changes

solar wood

• changes in precipitation patterns, ocean levels

wind • ozone depletion peat • acid rain

(primarily from coal power plant emissions)

– SO4 and NOx form, respectively, H2SO4

and H2NO3 in the atmosphere – These acids precipitate in rain water and

thus harm humans, animals, trees, crops, lakes

• Radioactive and toxic waste • Oil spills • Increased river temperatures from cooling water of

power plants • This list is not meant to be inclusive, but rather demonstrates the many different ways in which

human energy demands and the various energy sources impact the environment.


17

Example 1 Simple Steam Power Plant 10—1000 MWatts Power e.g. Memorial Drive @ Western Avenue, supplies steam to Harvard through a 2 mile series of tunnels beneath the Yard)

Steam power plant schematic, from R.E. Sonntag et al., Fundamentals of Thermodynamics, 5th ed. (Wiley, 1998)

A set of individual Processes that combine to complete an Energy Cycle 1. Fuel is combusted to produce thermal energy from chemical energy. 2. This is used to heat water, boil it to steam and superheat vapor at high pressure. 3. Superheated steam enters turbine and expands; doing work on the shaft of turbine →

generation of mechanical energy. 4. shaft drives an electrical generator to produce electrical energy. 5. Low pressure steam leaves turbine and condenses → transfers thermal energy to cooling

water. Require large quantity of coolant ⇒ Power plants often located near rivers and lakes ... thermal pollution concerns. 6. Pump pressurizes and circulates condensate 7. Hot waste gases do not contain sufficient thermal energy to boil water but they can be

used to preheat incoming air for combustion and raise water temperature close to boiling.

(sometimes called “regeneration” process)


18

Some Important Points to Note: • Concept of low grade heat vs high grade heat →hot waste gases and warm water vented to environment...why can’t we use this

energy? • Fluid in plant undergoes a thermodynamic cycle which is continually repeated. This thermal carrier or heat transfer fluid is usually high pressure steam, but CO2, liquid

sodium are also used (esp. in nuclear power plants). requirements • ability to convey a large quantity of heat per unit mass – specific heat Cp (kJ/kgK) “Sensible Heat” – phase change ∆H (kJ/kg) “Latent Heat” • ability to rapidly transfer heat into and out of fluid – thermal conductivity k (kW/Km) • ability to circulate fluid around power plant – low density (for pump and piping design) – low viscosity (viscous or frictional losses) • As we shall see later, the 2nd Law of Thermodynamics tells us that each operation is less

than 100% efficient. These inefficiencies multiply for the overall plant. Typical overall efficiency 30% — 40% →Fuel Requirements for a 1000 MW Power Plant = 2.4 × 1011 Btu/day coal: 9000 tons/day or 1 ‘unit train load’ (100 × 90 ton cars)/day oil: 40,000 bbl/day or 1 tanker/week natural gas: 2.4× 108 SCF/day (SCF = 1 standard cubic foot) Uranium 3 kg/day (as pure 235U) D-T Fusion 8 g/day (2H, 3H)


19

Example 2: Gas Turbine The basic principle of the gas turbine is to convert the chemical energy of fuel + oxygen to the mechanical energy of shaft rotation. When turnbines are used for stationary power generation, this mechanical energy is converted into electrical energy. When, as in the example shown here, turbines are used for jet propulsion, much of the mechanical energy is converted into the kinetic energy of the hot exhaust gases moving backwards, thereby producing thrust. Some of the energy is also used to compress the air entering the combustion region. (Later in this course, when we analyze power cycles, we will learn why this enhances the overall performance.) The compressed air is then mixed with fuel and ignited; the hot, high-pressure exhaust gases then expand down the turbine, flowing past the fan blades and performing “shaft work”. GE turbofan jet engine, from R.E. Sonntag et al., Fundamentals of Thermodynamics, 5th ed. (Wiley, 1998)


20

Example 3: Introductory energy analysis of windmills or wind-turbine machines

The basic principle of a windmill is to convert the kinetic energy of (rapidly) moving air first into kinetic (or mechanical) energy of the rotating windmill vanes and then via an electrical generator into electircal energy. A rather crude schematic is shown below.

Wind turbines arrayed in a row on a wind farm. These turbines, rated at 400 kW each, have diameters of 33 m and their axes are 30 m above ground. (Photo: U.S. Windpower)

Electric Generator

e -

current

Packet of airmoving atvelocity

v

v

tt+dt

D/2

kinetic energy of = 21

2 mv mass

volume densityairρ = =⎯⎯⎯⎯⎯⎯→ kinetic energy per unit = 212 ρv

mass m volume of air kinetic energy (of moving air) per unit time impinging on 22 2volume1 1

2 time 2 4Dπρ ρ= × = ⋅ ×v v v

the windmill 2 31

8 Dρπ= v cubic dependence on velocity is very important energy 2 31

time 8Power= Dρπ= v if all available kinetic energy of the oncoming wind

were converted into kinetic energy of the windmill.


21

Unfortunately, the efficiency of energy conversion is rather low. There are ‘losses’ since certainly not all of the kinetic energy of the wind may be extracted and the electric generator is typically 70—90% efficient at moving mechanical energy of a rotating shaft into electrical energy.

ASSUME: 30% overall efficiency (typical value for present generation of devices) Windmill Power 2 30.3

8 Dρπ= v

Question: What is the power output of a windmill with vanes D = 30 m? Assume v = 5 mph (8 km/hr) and compare the result with the case of an increased

windspeed of 20 mph (32 km/hr).

2

3

1 Joule 1 kg m1 Watt = = sec sec

3air 1.2 kg/mρ =

v = 8.0 km/hr. = 2.2 m/s POWER = 1396 W ≈ 1.4 kW v = 32 km/hr. = 8.9 m/s POWER × 43 ≈ 89.6 kW (cf. A large power station: l GW = 103 MW = 106 kW = 109 W) Two remarks (i) Because of the v3 dependence of the windmills optimum power output, there is a great

advantage to be gained by increasing the exposure to higher speed winds (within limits of course; you do not want to destroy the facility). Hence, placement of the windmills is crucial to their success.

(ii) California accounts for approximately 12% of the population of the U.S. 15% of the

electrical output of PG&E, California’s largest utility, is supplied by wind energy. (iii) Such a system of power generation is inherently extremely scaleable. Exercise: The majority of windmills are used for pumping water. Estimate the rate (gal/min) at which water can be pumped from a depth h = 30 m by this windmill in a wind of speed v = 5 mph.


22

Exercise: The majority of windmills are used for pumping water. Estimate the rate (gal/min) at which water can be pumped from a depth h = 30 m by a windmill (D = 30 m) in a wind of speed v = 5 mph. Given: The power output of a typical modern windmill is

2 30.38 airW Dρ π= v if 30% efficient (1)

NB In order to reduce confusion, it is useful in thermodynamics to indicate power by the

symbol W and think of it as “the rate of doing work” (the overdot indicates that this is a derivative with respect to time). Do not choose P because it can be confused with pressure.....

The unit of power is the Watt (1 W = 1 J/s) The water pumped from the well must have its potential energy charged by mgh (for a mass

m of water). ( )PE mgh∆ = (in Joules) (2)

However, we now have one expression in units of power and one in terms of energy. If we

let Q = volumetric flow rate = volume of H2O pumped per unit time; then the change of

potential energy in time δt is

( ) ( )2mass H Ovolume

PE gh Q tδ δ= × × ×

or the rate of change in potential energy (in J/s) is

( )water

PEQ gh

tδ

ρδ

= × × (3)

Assume: All the power (energy/time) generated by the windmill goes into pumping water. Equating (1) and (3) gives:

2

30.3 8

air

water

DQgh

ρ πρ

= v (4)

e.g At 5 mph (2.2 m/s) for 30 m diameter blades and a 30 m deep well, Q ≈ 1000 gpm.


23

Example 4: Fuel Cell The fuel cell converts the chemical energy of fuel + oxygen directly into electrical energy, thereby avoiding all the intermediate processes involving mechanical moving parts and their associated efficiencies. In the hydrogen fuel cell shown below, hydrogen enters at the anode side and oxygen enters at the cathode side. The hydrogen gives up its electrons at the anode electrode with the following reaction: 2H2 → 4H+ + 4e- These electrons flow through the potential difference between anode and cathode and perform electrical work. The hydrogen diffuses through an ion-exchange membrane and combines with oxygen at the cathode: 4H+ + 4e- + O2 → 2H2O. Because this is a very clean process (the only combustion products of a hydrogen fuel cell are water and heat), there is intensive R&D effort going into scaling it up and making it cost-effective. Currently fuel cells are used to produce power in outer space. Some buses powered by fuel cells are on the market, and automobiles powered by fuel cells are expected to hit the market in 2003 or 2004. One still must deal with where we get the hydrogen, and there can be significant pollution and inefficiencies associated with fuel production and transport.

Load

4e-

Anode_

Cathode+

4e-

Hydrogen

Gas chambers

Oxygen

Ion-exchange�membrane�

Catalytic�electrodes

4e-

4H+ 2H2OO2

H2O

2H2

4e-

4H+

The hydrogen fuel cell.


24

Example 5: Thermoelectric Refrigerator The thermoelectric refrigerator uses electrical work to transfer heat from one location to another. This device uses the “thermoelectric effect”, a phenomenon that occurs because electrons carry both electrical current and thermal energy. Two different materials with different coupling strengths between electrical current and thermal energy are used. Running current one way results in a net transfer of heat in one direction; running it the other way reverses the direction of net heat transfer. The CPUs of many desktop computers now generate so much heat that thermoelectric refrigerators are employed to keep them from overheating. One can employ a pre-existing temperature difference to create electrical current with the same device. Spontaneous heat flow from the hot junction to the cold junction drives the current. This is the principle behind a “thermocouple” temperature-measuring device, in which one records the voltage created from a well-calibrated pair of materials and thereby determines the temperature of the hot junction. Alternatively, one can use this voltage to perform electrical work as illustrated in the diagram on the right. Thermoelectric refrigerators and power-generating devices currently cannot compete economically with vapor-compression refrigeration cycles. However, intensive R&D on these devices continues.

Cold junctionHot junction

Heat transfer fromrefrigerated space

Heat transfer fromhigh-temperature body

Hot junctionCold junction Hot junctionCold junction

MetalMetalelectrodeselectrodes

Material AMaterial A

Material BMaterial B

Heat transfer to ambientHeat transfer to ambient

_ +

ii ii

Load

A thermoelectric refrigerator.

A thermoelectric power generation device.

introduction to energy and thermodynamics v4...

Documents