9/11/08 NOTES 9/9/08 POSTED QUESTIONS ABOUT …physics.wustl.edu/wimd/C5_9-11-08.pdfnotes 9/9/08 posted questions about power and energy? the three laws of thermodynamics ... a super-engine

EFFICIENCY AND THESECOND LAW OF

THERMODYNAMICS

9/11/08

NOTES 9/9/08 POSTED

QUESTIONS ABOUT POWER AND ENERGY?

THE THREE LAWS OF THERMODYNAMICS

1ST LAW: ENERGY IS CONSERVED.

2ND LAW: THERMAL ENERGY CANNOT BE TURNED INTO USEFUL WORK WITH 100% EFFICIENCY.

3RD LAW: AS THE ABSOLUTE ZERO OF TEMPERATURE IS APPROACHED, ALL THERMAL MOTION CEASES. (BUT WE CAN NEVER GET THERE!)

YOU CAN’T WIN.

YOU CAN’T BREAK EVEN.

YOU CAN’T GET OUT OF THE GAME.

HEAT ENGINES AND THE RISE OF WESTERN CIVILIZATION

~1ST CENTURY CE: HERO’S ENGINE

1769: WATT’S STEAM ENGINE

1824: CARNOT CYCLE

1877: NICOLAUS OTTO PATENTS A 4-STROKE INTERNAL COMBUSTION ENGINE

HERO OF ALEXANDRIA’S “ENGINE”

AEOLIPILE = BALL OF AEOLUS

WATT’S STEAM ENGINE

JAMES WATT 1736-1819

OTTO AND THE GASOLINE ENGINE

NICOLAUS OTTO 1832-1891

ANIMATION

THERMAL ENERGY

THERMAL ENERGY CAN BE THOUGHT OF AS A FORM OF KINETIC ENERGY- THE ENERGY OF MOLECULES MOVING RANDOMLY. WE DON’T KNOW THE ENERGY OF INDIVIDUAL MOLECULES- JUST THE TOTAL ENERGY

TEMPERATURE IS A MEASURE OF AVERAGE ENERGY: THE AVERAGE KINETIC ENERGY OF AN ATOM OR MOLECULE IS PROPORTIONAL TO ABSOLUTE TEMPERATURE T

ABSOLUTE TEMPERATURE IS MEASURED IN DEGREES KELVIN: KELVIN=CELSIUS+273 (K = C + 273).

ZERO DEGREES KELVIN IS ABSOLUTE ZERO, WHERE THERMAL MOTION STOPS.

ENERGY AND USEFUL ENERGY

ENERGY IS NEVER LOST, BECAUSE IT IS CONSERVED (FIRST LAW OF THERMODYNAMICS).

THERMAL ENERGY CAN BE WASTED, IN THE SENSE THAT IT MAY NOT BE AVAILABLE TO DO USEFUL WORK.

ONE FORM OF THE SECOND LAW OF THERMODYNAMICS IS THAT IT IS IMPOSSIBLE TO CONVERT THERMAL ENERGY INTO USEFUL WORK WITH 100% EFFICIENCY.

A THOUGHT EXPERIMENT

HEAT ENGINES USE TEMPERATURE DIFFERENCES TO TURN THERMAL ENERGY INTO USEFUL WORK.

ONCE THE TEMPERATURE DIFFERENCE IS GONE, THE ENERGY IS STILL THERE, BUT WE CANNOT TURN IT INTO USEFUL WORK.

THIS IS THE DIFFERENCE BETWEEN A HOT GAS PUSHING A PISTON (THERMAL ENERGY CONVERTED TO MECHANICAL ENERGY) AND FREE EXPANSION OF THE SAME HOT GAS.

ENTROPY AND ORDER

ENTROPY IS A THERMODYNAMIC QUANTITY THAT MEASURES THE DISORDER OF A THERMAL SYSTEM

GENERALLY, THE HIGHER THE TEMPERATURE, THE MORE DISORDERED (RANDOM) A SYSTEM IS.

ANOTHER FORM OF THE SECOND LAW OF THERMODYNAMICS IS THAT THE ENTROPY OF A CLOSED SYSTEM NEVER DECREASES!

THE SECOND LAW ALSO STATES THAT IT IS ONLY POSSIBLE TO PERFORM WORK BY TRANSFERRING HEAT FROM HOT BODIES TO COLD

STEAM ENGINE

WATER IS CONVERTED TO STEAM BY BURNING WOOD OR COAL

STEAM PUSHES PISTON BACK AND FORTH, TURNING WHEEL TO DO WORK

STEAM CONDENSES BACK INTO WATER AND SO ON ...

HEAT ENGINES

A HEAT ENGINE IS AN ENGINE POWERED BY THERMAL ENERGY.

EXAMPLES INCLUDE AUTO ENGINES, COAL-FIRED POWER PLANTS, AND NUCLEAR REACTORS.

WE REPRESENT AN ABSTRACTION OF A HEAT ENGINE AS HAVING THREE PARTS: A HEAT SOURCE, AN ENGINE, AND A HEAT SINK.

HOT

COLD

W

Qh

Qc

HEAT ENGINES 2

HOT

COLD

W

Qh

Qc

Qh = W +Qc

1ST LAW:

EFFICIENCY:

! =WQh

= 1! Qc

Qh

2ND LAW- NO HEAT ENGINE IS 100% EFFICIENT:

! < 1 Qc != 0

REVERSIBLE ENGINES

HOT Th

COLD Tc

W

Qh

Qc

REVERSIBLE ENGINES CAN RUN FORWARDS AND BACKWARDS. THEY ARE MODELS FOR REFRIGERATORS AND HEAT PUMPS. THEY ARE ALSO CALLED CARNOT ENGINES.(FRICTIONLESS SO IDEALIZATION)

KEY FACT FOR REVERSIBLE ENGINES:

Qc

Qh=

Tc

Th

! = 1! Qc

Qh= 1! Tc

Th

NOTE: MUST USE ABSOLUTE TEMPERATURE!

NO SUPER-ENGINES EXIST!

A SUPER-ENGINE IS A HEAT ENGINE MORE EFFICIENT THAN A REVERSIBLE ENGINE

WE WILL PROVE THAT THE EXISTENCE OF A SUPER-ENGINE WOULD VIOLATE THE 2ND LAW

THEREFORE, A REVERSIBLE ENGINE IS THE MOST EFFICIENT ENGINE

HOT

COLD

W

Qh

Qc

PROOF BY CONTRADICTION

HOT

COLD

SUPER

W’Qh

Qc’

REV

W

Qh

Qc

W’>W

SUPER + REVERSIBLE=SUPER-DUPER ENGINE

EFFICIENCY BOUND FOR HEAT ENGINES

HOT

COLD

W

Qh

Qc

!! !rev = 1" Tc

Th

THIS IS AN ULTIMATE, IRREVOCABLE BOUND ON HEAT ENGINE EFFICIENCY

CERN

LHC

STANDARD MODEL

THREE FORCES

12 FERMIONS

BOSONS TRANSMIT FORCE

COST OF THE LHC $3.8X109

IS IT WORTH IT?