01d - the concept of energy

8/12/2019 01D - The Concept of Energy

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The World of Energy

1. 4 . The Concept of Energy

Chapter 1 World Energy Overview


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The mystery and history of

energyThermodynamics: Not quite whatwe were taught it is, in unusualregimesGoing beyond, to more efficientways to use energy

The Concept of Energy


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Easy Question:What is Energy?


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Energy is one of the most incredible

concepts to emerge from the human mind

Is it a discovery or an invention?

Energy is an abstract concept that tiestogether a remarkable range of dissimilarhuman experiences

And does it in a way with astoundingquantitative predictability!

Can you say, tersely, what energy is ?


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It seems an obvious concept, even to

obvious at all for a long, long timeBacon, Galileo: heat is motionRumford: mechanical work converts intoheat

in motion?

What energy is ?


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establish an equivalence between heat and

lightBut he recognized two kinds of transfer,essentially radiation and convectionLavoisier & Laplace (1783): whether caloric

Commonality of heat and light


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Is it mass x velocity, or mass x (velocity)2

?

This was the conflict between the Leibnitziansand Cartesians

At that time, it was inconceivable that bothcould be valid!

An indication of the problems: A controversy


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Recognize latent heats of phase changes, androle of heat in changing densities

Rumford: heat has no weightYoung: heat and light are related

Leslie (1804): distinguishes conduction,convection and radiation and uses the term

How to account for heat that


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Fourier: Quantifies Heat

Heat capacityInternal conductivityExternal conductivity (radiation,convection)Quantification of heat flow andtransfer, with differential eqns.


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The Steam Engine: Watt

The external condenserThe direct measure of pressure as afunction of volume, to determineefficiency (the Indicator Diagram, pvs. V)The use of high pressures andtherefore of high temperatures


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The Breakthrough, stimulated by applications

form

In effect, Energy is conserved !

Carnot


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More from Carnot

The invention of the reversible engineand the demonstration that it is themost efficient engine possible

The determination of that maximumefficiency, and that no engine can dobetter


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J. R. Mayer (1842-48) stated theprinciple explicitly, and included

energy from gravitational acceleration

Quantified the mechanical equivalentof heat

Included living organisms

Aha! Conservation of Energy!


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Brought electromagnetic energy intothe picture

Measured mechanical equivalent ofheat

Showed that expansion of a gas into avacuum does no work

Joule, of course!


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Motivation: How little fuel must Iburn, in order to pump the water outof my tin mine?

Carnot confronted and solved this

problem, but the great generalizationcame later

Creation of Thermodynamics


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Two kinds of variables: Statevariables , e.g. pressure p, volume V,temperature T

Process variables , energy transferred

either as heat Q , or as work W.

The Law: the change of energy, E= Q W , whatever the path

The First Law


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This law states conservation of energy

Whatever the path, only the end pointsdetermine the energy change

If the final and initial states are thesame, the energy of the system isunchanged

The First Law


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The randomness--or entropy--or thenumber of microstates the system can

explore--never decreases spontaneously

Decreasing entropy requires input of

work

Corollary: Max efficiency is

(T high Tlow )/ Thigh

The Second Law


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The Third Law

There is an absolute zero oftemperature, 0 o K or 273 o C

You can never get there; it is asunreachable as infinitely hightemperature

But we can now get pretty cold, as lowas 10 8 o K


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Thermodynamics is, among all sciences, theone most likely to be valid

Hence we can think of thermodynamics asthe epitome of general scientific law

But we sometimes lose sight of what is trulygeneral and what is applicable for onlycertain kinds of systems or conditions

Einstein


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Thermodynamics has two kinds of statevariables:

Intensive , independent of amount, e.g.Temperature, pressureExtensive , directly proportional to amount,e.g. mass, volume

A common, elegant presentation


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Also two kinds of relations

General laws, the Laws ofThermodynamics

Relations for specific systems, e.g.equations of state , such as the ideal

gas law, pV = nRT, giving a thirdquantity if two are known (Rememberthat one?)


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How many variables can we control? Fora pure substance, we can change three ,

e.g. pressure, temperature and amountof stuff Fix the amount and we can vary only

twoThe equation of state tells us everythingelse

Degrees of freedom


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Equations of State are usually not simpleThe equation of state for steam,used daily by engineers concernedwith real machines, requiresseveral pages to write in the formthey use it!Not at all like pV=nRT!

Equations of State


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Generalize to find optimal performancesThermodynamic Potentials are the quantities that

tell us the most efficient possible energy use forspecific kinds of processes, different potential fordifferent processesAll use the infinitely slow limit, as Carnot did, to

do best

Equations of State


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Some Jargon

Names for some thermodynamic potentials

The change in the appropriate potential isthe minimum work we must do, or themaximum we can extract, for that process


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The Gibbs phase rule: relates the number ofdegrees of freedom, f , to the number ofcomponents c (kinds of stuff) and the number ofphases present in equilibrium, p :

f = c p + 2, the simplest equation inthermodynamics, perhaps in all science

The amount of each component can bevaried at willEach phase, e.g. liquid water, ice or watervapor, has its own equation of state,implying a constraint for each phaseOne substance, one phase, yields twodegrees of freedom, as we saw

The subtle profundity of thermodynamics


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Water vapor: any T or p is okay


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But, if there is liquid also:


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The f comes by definitionThe c is obviously our choice

The p is the number of constraintsHence all these are easy and obvious

2 that is profound! Only

experience with nature tells uswhat that number is!

phase rule?


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Very big systems--galaxy clusters--and verysmall systems--atomic clusters--should all be

describable by thermodynamics

cluster? Gravitation , of course

The real generality of thermodynamics


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two objects?

Inversely proportional to distance ofthe objects,Directly proportional to the productof their masses, m 1 x m 2 !This is not linear in the mass!Astronomers created nonextensivethermodynamics to deal with this.

Gravitational Energy


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Another case where thermodynamics

Very small systems, e.g. nanoscalematerials, composed of thousands or even

just hundreds of atomsThe distinction between component andphase can be lost, so the Gibbs phase ruleloses meaningWith very small systems,

Two phases may coexist over a band ofpressures and temperatures, not just along asingle coexistence curveMore than two phases can exist in equilibriumover a band of conditionsPhase changes are gradual, not sharp

Consistency of Thermodynamics

C d th d i f


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Close to equilibrium, Lars Onsager showed a

Further away from equilibrium, one needsmore variables to describe the system

Can we guess what variables to use?Sometimes, not always

Can we do thermodynamics away fromequilibrium?


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Create a thermodynamics for processes thatmust operate in finite time

We can, for many kinds of finite-timeprocesses, define quantities like traditional

thermodynamic potentials, whose changesgive the most efficient or effective possible useof the energy for those processes


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Finite-time potentials

It is possible to define and evaluate these, forspecific processes, to learn how well a processcan possibly perform

It is then possible to identify how, in practice,we can design processes to approach the


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Example: the automobile engine

The gas-air mix burns, the heat expands thegas, driving the piston down, so the pistons goup and down

The connecting rod links piston with driveshaft,changing up-down motion into rotation

Does the piston, in an ordinary engine, followthe best path to maximize work or power? NO!


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Change the time path to make the pistonmove fastest when the gas is at its highesttemperature!

So how can we do better?


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Changing the mechanical link would improveperformance about 15%

Red: conventional time path of piston; black:ideal, given a maximum piston speed

So how can we do better?


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One other example

Distillation, a very energy-wastefulprocess

But make the temperature profilealong the column a control variableand the energy waste goes way downOne such column is going up now, inMexico


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Energy is an amazing concept, subtle,powerful, elegant, general,

Its quantitative, predictive power is perhapsthe epitome of what science is about!It is important for all its aspects, from the

most basic to the most practical and applied

So what have we seen?

01d - the concept of energy

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