Energy and the Environment

Energy and the EnvironmentSpring 2014

Instructor: Xiaodong ChuEmail ： [email protected]

Office Tel.: 81696127Mobile: 13573122659

mailto:[email protected]

Thermodynamic Principles: The Forms of Energy

• The mechanical energy of macroscopic bodies– Newtonian mechanics identifies two forms of energy, the kinetic

energy and the potential energy

– The total energy

– Without any other force applied to the body, the energy E is unchanged, which is called as the principle of conservation of energy

21

2KE MV

constantE KE PE

r

rrrF

ref

dPE }{


Potential-kinetic energy transformations of a hydroelectric power station


• The internal energy of a macroscopic body– The matter of a macroscopic body is composed of microscopic atoms

and/or molecules– The aggregate energy of all the molecules is called the internal energy

U– Consider the total energy of microscopic molecules to be the sum of

the kinetic energies of their motion and the potential energies of their intermolecular forces

– Changes in the internal energy can be measurable by changes in temperature, pressure, and density, which are called thermodynamic state variables


• Chemical and nuclear energy– Atoms of molecules are held together by strong forces that resist

rearrangement of the atoms and to disassemble a molecule into its component atoms usually requires the expenditure of energy, so that the molecules of a body may be considered to possess an energy of formation related to how much energy was involved in assembling them from their constituent atoms

– A similar energy change accompanies the formation of new atomic nuclei in the fission of the nuclei of heavy elements or the fusion of light ones and because the binding forces that hold nuclei together are so much larger then those that hold molecules together, nuclear reactions are much more energetic than molecular ones

• The amount of chemical energy typically released (or converted) in a chemical explosion is: 5 kJ for each gram of TNT

• The amount of nuclear energy typically released by an atomic bomb is: 100,000,000 kJ for each gram of uranium or plutonium


• Electric and magnetic energy– Molecules that possess a magnetic or electric

dipole moment （偶极矩） can store energy when they are in the presence of a magnetic or electric field, in the form of magnetic or electric polarization of the material


• Total energy– The various forms of energy that can be possessed

by a material body can be added together to define a total energy E

– In any practical process, just a few of the energy forms are significant

– The laws of thermodynamics is expressed through the total energy E

magelnucchem EEEEUPEKEE

Thermodynamic Principles: Work and Heat Interaction

• Thermodynamics deals with the interaction of a thermodynamic material system and its environment

• There are two different modes of interaction, i.e., the work interaction and the heat interaction

• Both heat and work interactions may occur simultaneously• Neither the work interaction or the heat interaction is a form

of energy, but only a transaction quantity accounting for the character of the exchange of energy between a thermodynamic system and its environment


• Work interaction– In thermodynamics, positive work is defined to be the product of the force exerted by a system

on the environment times any displacement of the environment that occurs while the force is

acting– The increment of work

enendrFdW


– Examples of a work interaction• Gas contained in a circular cylinder: if the piston is

displaced an incremental distance dren with the force pA exerted on that portion of the movable piston (the environment), the positive work increment dW is

pdVAdrppAdrdW enen )(


• Shaft of a turbine: if an electric generator attached to the turbine rotates through an increment of angle dθen with a torque Ten exerted on it, the work increment is

enendTdW


• Heat interaction– A temperature difference between a system and

its environment is required for a heat interaction– The increment of heat

enendTCdQ

Thermodynamic Principles: The First Law

• The first law of thermodynamics is an energy conservation principle

• The increment in system energy dE equals the increment in heat dQ transferred to the system minus the work dW done by the system on the environment

• In another word, the sum of the system energy change dE, the work dW, and the heat —dQ added to the environment is zero

dWdQdE

0)( dQdWdE

Thermodynamic Principles: The First Law

• The first law can be expressed in integral form besides differential form

• There are many different processes that can bring about the same change in energy of the system from the same initial to final states, each distinguished by different amounts of heat and work

f

i

f

iif dWdQEE

Thermodynamic Principles: The Second Law

• Is it possible to design a system converting all of the fuel energy to work?

• The second law of thermodynamics states that it is not possible to devise a cyclic process in which heating supplied from a single source is converted entirely to work

• Some consequences of the second law– There exists an absolute temperature scale, denoted by T , which is

independent of the physical properties of any substance and which has only positive values

– There is a thermodynamic property called entropy, denoted by S, whose incremental change is equal to the heat interaction dQ divided by the system temperature T for any incremental process in which the system temperature remains spatially uniform

revT

dQdS )(

Thermodynamic Principles: The Second Law

– In any process, dS is equal to or greater than the ratio dQ/T , which is called the inequality of Clausius, and in a process for which dQ = 0, which is called an adiabatic process, the entropy may remain the same or increase but may never decrease

• The third law of thermodynamics is an additional principle that is closely related to the second law, which states that the entropy of all thermodynamic systems is zero at the absolute zero of temperature

Thermodynamic Principles: Thermodynamic Properties

• Intensive properties （强度性质） : pressure p and temperature T are called intensive properties because their values are not proportionate to the mass of a fluid sample but are the same at all points within the sample

• Extensive properties （广度性质） : the energy E, volume V, and entropy S are extensive properties in that their values are directly proportionate to the mass of a fluid sample

• Specific extensive properties （比广度性质） : we divide an extensive property by the mass M of fluid, then the corresponding ratio is independent of the amount M

M

Ss

M

Vv

M

Ee , ,


• Particular combinations of the properties p, T, v, e, and s– Enthalpy （焓） is defined as

The amount of heat added in a constant pressure process （恒压过程） is equal to the increase in enthalpy of the material

The ratio of the increase in enthalpy, at fixed pressure, to the increment of temperature experienced in this process is called the constant-pressure specific heat（恒压比热）

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pdvdqdwdqde

)()(

pveh

ppp T

Tph

T

Tpqc

},{},{


The ratio of the energy increase to the concomitant temperature increase is called the constant-volume specific heat （恒容比热） ,

considering a heating process at fixed volume where no work is done and the increase in energy de is equal to the heat increment dq

vvv T

Tpe

T

Tpqc

},{},{


• Particular combinations of the properties p, T, v, e, and s– Gibbs’ free energy is defined as

For a process that proceeds at constant temperature and pressure, the amount of work done by a system cannot exceed the reduction of free energy

The free energy is a useful thermodynamic function in cases of chemical or phase change

TspveTshf


• It is possible to express the relationship between these properties in differential form since for a reversible process, dq = Tds

dfsdTdh

vdpdh

pdvdeTds

Thermodynamic Principles: Steady Flow

• Many thermodynamic systems incorporate components through which a fluid flows at a mass flow rate invariant in time, which is called steady flow

• If the flow is steady, the first law can be expressed in a form that relates thermodynamic properties of the inflowing and outflowing fluid streams with the rates at which heat is added to and work is done by the fluid within the component

ThenWQhmhm inout

wqmWmQhh inout //

Thermodynamic Principles: Heat Transfer and Heat Exchange

• The time rate of exchange of work and heat quantities determine the mechanical or thermal power that can be produced

• In most cases of steady heat transfer from a hot to a cold environment, the time rate of heat transfer

where u is the heat transfer coefficient, A is the surface area, and uA is called the thermal conductance

• To obtain high value of u, one should use a thin layer of good heat conductor; to get low value of u, one should use a thick layer of thermally insulating material

)( ch TTuAQ

Thermodynamic Principles: Heat Transfer and Heat Exchange

• Heat exchangers are passive devices accomplishing a transfer of heat, usually between two streams of fluids, one hot and the other cold

• The functioning of heat exchangers involves loss of mechanical power, reduced thermodynamic efficiency, and increased economic cost

• The transfer of heat at finite rates in thermodynamic systems inevitably incurs performance penalties that cannot be reduced to zero except by the expenditure of infinite amounts of capital

Thermodynamic Principles: Combustion of Fossil Fuel

• The most common fossil fuels are hydrocarbons, i.e., mixture of molecules composed of carbon and hydrogen– Upon their complete combustion, the carbon is oxidized to

carbon dioxide and the hydrogen to water vapor – The energy made available in this oxidation is the net

amount released when the carbon and hydrogen atoms are separated from each other and combined with oxygen to form carbon dioxide and water


• Denoting a hydrocarbon fuel molecule as CnHm, the molecular rearrangement can be represented by the reaction

• The ratio of the number of oxygen molecules to the number of fuel molecules, n + m/4, is called the stoichiometric ratio and it can be expressed as a mass ratio as

which lies in the range between 8/3 (for pure carbon) and 7.937 (for pure hydrogen)

OH)2

(COO)4

(HC 222

mn

mnmn

mn

mn

008.112

832

mass fuel

massoxygen


• The stoichiometric ratio is more usefully expressed in terms of the ratio of air mass to fuel mass by multiplying the ratio of the mass of air to the mass of oxygen in air, which is 4.319

• If less air is available than is required, not all of the carbon

or hydrogen will be fully oxidized and some amount of CO, solid C, or H2 may be present while not all the available chemical energy is released in the combustion process

mn

mnFA st 008.112

832319.4)/(

mass fuel

massair


• Fuel heating value ( 燃料热值 )– When a mixture of fuel and air is burned, the temperature of

the combustion products formed is much higher than that of the fuel–air mixture

• Heat may be transferred from the hot combustion products to a colder fluid

• The amount of heat available for this purpose is called the fuel heating value and is usually expressed in energy units per unit mass of fuel


– Consider a combustion chamber of a gas turbine power plant that is supplied with a steady flow of a fuel-air mixture (reactant)

• If fuel is burned at constant pressure and no heat is lost, i.e., adiabatic and workless, by recalling the equation

• The product gas enthalpy hp{Tp, pr} will equal the reactant stream enthalpy hr{Tr, pr}, where Tp is called the adiabatic combustion temperature

WQhmhm inout

},{},{ rrrrpp pThpTh


• If the hot product gases are cooled at constant pressure to the reactant temperature, then the heat removed per unit mass of product gas will be equal in magnitude to the reduction in enthalpy hp{Tp, pr} - hp{Tr, pr} = hr{Tr, pr} - hp{Tr, pr}

• Multiplying by the mass flow rate of products divided by the mass flow rate of fuel, we obtain the fuel heating value

• If the H2O formed in the combustion product is in the vapor phase, then the fuel heating value is called the lower heating value whereas it is called the higher heating value if the H2O is in the liquid phase

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prr pThpTh

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mpTFHV


Thermodynamic Principles: Ideal Heat Engine Cycles

• Generating mechanical power from fossil fuel must utilize the combustion process to change the temperature and/or pressure of a fluid and then find a way to use the fluid to make mechanical work by moving a piston or turning a turbine– The first and second laws of thermodynamics limit the amount of

work that can be generated for each unit mass of fuel used, and those limits depend upon the details of how the fuel is used to create power

– Analyze ideal devices in which a fluid is heated and cooled, and produces or absorbs work, as the fluid moves through a cycle and such a device can be called a heat engine


• The Carnot cycle– The Carnot cycle is illustrative of the second law limits on the simplest

of heat engine cycles– It is sustained by two heat reservoirs, a hot one of temperature Th and

a cold one of Tc

– Consider the heat engine to be a cylinder equipped with a movable piston and enclosing a fluid of unit mass

– The cycle consists of four parts: two expansions and two compressions

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c

c

h

h

c

c

h

h

T

q

T

q

T

qS

T

qS

SS

4321

4321

,


• Reversible isothermal expansion of the gas at the "hot" temperature (1 to 2)

• Reversible adiabatic expansion of the gas (2 to 3) • Reversible isothermal compression of the gas at the "cold"

temperature (3 to 4) • Isentropic compression of the gas (4 to 1)


– The thermodynamic efficiency of the Carnot cycle to be

the thermodynamic efficiency depends only upon the temperatures of the two reservoirs and not at all upon the properties of the fluid used in the heat engine

– The amount of net work w that the heat engine delivers does depend upon the fluid properties and the amount of expansion

the net work is equal to the area enclosed by the cycle path in the T –s plane

h

c

hth T

T

q

w 1

w pdv Tds


– For Carnot cycle, the thermodynamic efficiency is improved by supplying the heat qh to the engine at the highest possible temperature Th

– For a fuel burning in ambient air and supplying this heat to the hot reservoir, Th could not exceed the adiabatic combustion temperature Tad and only a fraction of the fuel heating value could be added to the hot reservoir, that fraction being approximately (Tad − Th)/(Tad − Tc)

which has a maximum value of

cad

had

h

c

TT

TT

T

T1

1/

1/

had

cad

TT

TT


– A possible plan for increasing the efficiency would be to employ a large number of Carnot engines, each operating at a different hot reservoir temperature Th but the same cold reservoir temperature Tc

– The combustion products of a constant-pressure burning of the fuel would then be brought into contact with successively cooler reservoirs, transferring heat amounts dh from the combustion gases to produce work amounts dw, where

and by integrating it, we obtain

)(1 sThddhT

Tdw c

h

c

1)/(

)/ln(1

cad

cad

TT

TT


• An example of a Carnot cycle of a steam power plant– If the temperature of steam produced by the boiler is 600oC and that

of water from the condenser is 25oC, neglecting the work conducted on the pump, what is the efficiency?


Adiabatic Expansion

Isothermal Compression

AdiabaticCompression

Isothermal Expansion

Hurricane as a Carnot cycle

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