• • René F. Gastelumendi

• October 16, 2008•

Presentation prepared for the Science teachers of the Universidad Peruana de Ciencias Aplicadas, UPC

Entropy = Measures the energy that has lost its capacity to do

work

Genesis of the idea

• Acknowlegment of the imposibility of the construction of an perpetual motion engine.

Perpetual Motion Engine Types:

Type I: Which accomplishes motion with out the input of energy.

Example…

… of the First Type: (Motion with out energy being furnished)

Perpetuum Mobile by Villard de Honnecourt (circa 1230).

=

Perpetual Motion Engine Types:

Type II: Which obtains motion from only a source of heat energy and transforms all of that energy into motion.

Example…

...of the Second Type: (movement from only one heat source)

Heat

Work

Instead of…

Heat(Hot) Work

Cold

Joule’s Experiment

Joule’s Experiment

•Stablished the Mechanical Equivalence of Heat*

•Paved the way to the understanding that all of the mechanical energy can be transformed into heat energy

*(4.18 J per calorie)

But, on the other hand, when transforming caloric energy to mechanical, contrary to the inverse process, part of the high

temperature energy is always transformed in low temperature energy.

Heat(High Temperature)

Work

Heat(Low Temperature)

An Assymetry in Nature is Found

We pay a Tax to Nature

The Assymetry: All of Work can be transformed into Heat, but, all of Heat cannot be transformed into Work.

“Nature accepts the equivalence bewteen Heat and Work, but demands a contribution each time that Heat is transformed into Work”

Atkins

“Nature does not tax the conversion of work into heat: we can happily waste what we have earned with our work by means of friction, and, moreover, do it completely. It is only Heat that cannot be converted in the same way. Heat pays taxes; Work does not.

Atkins

First and Second Law of Thermodynamics

• First Law: The Energy in the Universe is constant. It can only be transformed.

• Second Law:– It is imposible to convert Heat completely into

Work and in every engine, there must always exist a cold sink.

– Spontaneously, Heat is always transmited from the hottest body to the coolest body

Sadi Carnot(1876 – 1832)

Carnot’s Cycle(Represents an Ideal Engine)

It’s a reversible process: Whereasworking as a motor (I to IV) oras a refrigerator (IV to I), the processesare equivalent.

Carnot´s Engine• Moreover, a more efficient engine cannot be

constructed (working between the same two temperatures)

(Motor) (Refrigerator)

Carnot´s Engine Efficiency

H

LH

TTT

e

Understanding of Thermodynamicsin mid-Nineteenth Century

• Heat is a form of energy, and has a mechanical equivalence (Joule). This corresponds to the First Law of Thermodynamics

• Thermal and Thermo-mechanical procesess are essentialy energy transformations.

• Nevertheless there exists a bias in Nature such that, energy transformed irreversibly, cannot be again transformed completely, because it has been dissipated (friction, percussion).

Enters Rudolf Clausius(1822 – 1888)

Clausius’ Great Contribution• With respect to Carnot’s Engine,

cuantifies and distinguishes the meaning of the quotientQ /T (Caloric energy / Temperature)

when Heat is transformed(a) by virtue of only passage from a higher to a lower temperature, and (b) by virtue of performing Work between higher and a lower temperatures

…and determines that both transformations are equivalent

2

2

1

1

TQ

TQ

Transformation of Energy, Q, into Work, between T1 and T (T1 greater than T)

Transformation of Energy, Q between T2 and T (T2 greater than T),w/o performing Worki.e, by conduction.

In thermodynamics, when an expression like the one above is encountered, where a property is determined only from the initial and final conditions, one concludes that a new Termodynamic function has been found.

02

2

1

1 TQ

TQ

• Clausius demonstrated the existence of that function by means of a secuence of Carnot Engines:

0TdQ

For a reversible process

…and called it “Entropy”

• He took form Greek the word en-tropein, whose meaning is “transformation content” and “tweaked” it to resemble the word Energy; whence “Entropy” appeared.

0TdQ

For a ireversible process

…because procesess in Nature are not reversible, Entropy always increases…

Enters Ludwig Boltzman(1844 – 1906)

k = Boltzman constant = 1.38066 J K-1

= R, the gas constant divided by NA, Avogadro’s Number

= N° de microstates of the thermodynamic state

lnkS

The expression helps us to interpret Entropy as a meassure of the “multiplicity” associated with the states of systems.

“If a system can reach a given state in many ways, then that state is more probable than the one that can be reached in fewer ways.”

lnkS

Millon pounds metafor

A million pounds together can do more“Work” that the same quantity distributedamong a million persons; in this last case,money has increased its “Entropy”.

The End

Please look for references in the next slide

References

• From Watt to Clausius by D.S. Cardwell. Cornell University Press

• The Mechanical Theory of Heat by Rudolf Clausius, re-printed by Bibliobazaar

• Termodynamics and The Free Energy of Chemical Substances by Lewis and Randall, 4ta edición. McGraw-Hill

• A Treatise on Thermodynamics by Max Plank, 3ra Ed., Dover Publications.