Physics 41 Last Lecture

Entropy and the Heat Death of the Universe

Important Concepts

Heat Engines

Refrigerators

Important Concepts

2nd Law of Thermo

• Heat flows spontaneously from a substance

at a higher temperature to a substance at a

lower temperature and does not flow

spontaneously in the reverse direction.

• Heat flows from hot to cold.

• Alternative: Irreversible processes must

have an increase in Entropy; Reversible

processes have no change in Entropy.

• Entropy is a measure of disorder in a system

2nd Law: Perfect Heat Engine Can NOT exist!

No energy is expelled to the cold reservoir

It takes in some amount of energy and does an equal amount of work

e = 100%

It is an impossible engine

No Free Lunch!

Limit of efficiency is a Carnot Engine

Second Law – Clausius Form

It is impossible to construct a

cyclical machine whose sole effect

is to transfer energy continuously

by heat from one object to another

object at a higher temperature

without the input of energy by

work.

Or – energy does not transfer

spontaneously by heat from a cold

object to a hot object.

Section 22.2

Heat Pumps and Refrigerators Heat engines can run in reverse

This is not a natural direction of energy transfer

Must put some energy into a device to do this

Devices that do this are called heat pumps or refrigerators

energy transferred at high tempCOP =

work done by heat pump

h

heating

Q

W

energy transferred at low tempCOP =

work done by heat pump

C

cooling

Q

W

A heat pump, is essentially an air conditioner installed backward. It extracts energy from colder air outside and deposits it in a warmer room. Suppose that the ratio of the actual energy entering the room to the work done by the device’s motor is 10.0% of the theoretical maximum ratio. Determine the energy entering the room per joule of work done by the motor, given that the inside temperature is 20.0°C and the outside temperature is –5.00°C.

Carnot cycle

0.100h hQ Q

W W

293 K0.100 0.100 1.17

293 K 268 K

h h

h c

Q T

W T T

1.17 joules of energy enter the room by heat for each joule of work done.

energy transferred at high tempCOP =

work done by heat pump

h

heating

Q

W

Heat Pumps

Refrigerators

Reversible and Irreversible Processes The Arrow of Time! Play the Movie Backwards!

Entropy

The Maximum Efficiency

H

h h

h c

Q TCOP

W T T

c cC

h c

Q TCOP

W T T

and 1c c c

c

h h h

Q T Te

Q T T

H

h h

h c

Q TCOP

W T T

c cC

h c

Q TCOP

W T T

Entropy and Heat

The original formulation of entropy dealt with the transfer of energy by heat in a

reversible process.

Let dQr be the amount of energy transferred by heat when a system follows a

reversible path.

The change in entropy, dS is

The change in entropy depends only on the endpoints and is independent of the

actual path followed.

The entropy change for an irreversible process can be determined by calculating

the change in entropy for a reversible process that connects the same initial and

final points.

rdQdS

T

Section 22.6

DS in a Free Expansion

Consider an adiabatic free expansion.

This process is irreversible since the

gas would not spontaneously crowd

into half the volume after filling the

entire volume . Q = 0 but we need to find Qr

Choose an isothermal, reversible

expansion in which the gas pushes

slowly against the piston while energy

enters from a reservoir to keep T

constant.

1f fr

ri i

dQS dQ

T TD

Section 22.7

Since Vf > Vi , DS is positive

This indicates that both the entropy and the disorder of the gas increase as a result of the irreversible adiabatic expansion . ln f

i

VS nr

VD

1f fr

ri i

dQS dQ

T TD

Entropy increases when: • Temperature increases • Q flows into the system • Volume increases • Pressure decreases??

Entropy on a Microscopic Scale

We can treat entropy from a

microscopic viewpoint through

statistical analysis of molecular

motions.

A connection between entropy and

the number of microstates (W) for a

given macrostate is

S = kB ln W

The more microstates that

correspond to a given

macrostate, the greater the

entropy of that macrostate.

This shows that entropy is a measure

of disorder.

Section 22.8

Heat Death of the Universe

Ultimately, the entropy of the Universe should reach a maximum value. At this value, the Universe will be in a state of uniform temperature and density. All physical, chemical, and biological processes will cease.

The state of perfect disorder implies that no energy is available for doing work. This state is called the heat death of the Universe.

Big Bang Cosmogenesis

The Stellar Age

Stars Rule for a Trillion Years

In about 5 billion years,

Our Sun will swell into a cool Red Giant,

engulfing Mercury, Venus and possibly Earth!

The Degenerate Age After about 100 trillion, years, the stars are dead.

By 1037 years, the material in the "Local Galaxy"

consists of isolated stellar remnants and black holes.

Everything is cold and dark.

The Black Hole Age

All the stars turn into black holes.

After about 10100 years, all the black holes are gone.

The Dark Era

The remaining black holes evaporate: first the small ones, and

then the supermassive black holes. All matter that used to

make up the stars and galaxies has now degenerated into

photons and leptons.

Boltzmann was subject to rapid alternation of depressed moods with elevated, expansive or irritable moods, likely the symptoms of undiagnosed bipolar disorder. On September 5,

1906, while on a summer vacation in Duino, near Trieste, Boltzmann hanged himself during an attack of depression. He is buried in the Viennese Zentralfriedhof; his tombstone

bears the inscription.