Entropy

Time’s Arrow

Objectives

• Explain the tendency of matter and energy to spread out over time.

• Identify entropy changes in familiar processes.

Poll Question

I think I know what “entropy” means.

A.True.

B.False.

The Flow of Matter

particles disperse

Gas Molecule in a Box

No energy transfer to walls: elastic collisions

Gas Molecule in a Box

Double the size of the box!

Gas Molecule in a Box

Double the size of the box!

What portion of the time will the molecule spend in the original volume (left half of the box)?

a. Allb. Half

c. noned. 75%

Poll Question

What portion of the time will the molecule spend in the original space if we quadruple the volume of the box?

Poll Question

What portion of the time will the molecule spend in the original space if we quadruple the volume of the box?

a. Allb. Half

c. 1/3d. 1/4

Poll Question

What is the probability that the molecule will be in the original space at any given time?

a. 1b. 1/2

c. 1/3d. 1/4

V

V/4

Poll Question

Two Molecules (Poll)What is the probability that both will be in the left half of the container at the same time?

a. 1b. 1/2

c. 1/4d. 0

Three Molecules (Poll)What is the probability that all three will be in the left half of the container at the same time?

a. 1/2b. 1/3

c. 1/4d. 1/8

V

Whiteboard Work1.What is the probability that all N will be

in the given sector of the container at the same time?

xV

Expansion Summary

Random motions cause particles to spread out. The chance that they will randomly come back together decreases tremendously as the number of molecules increases.

Spreading out is irreversible.

Group It!

Discuss all succeeding poll questions with your group before answering.

The Flow of Energy

energy disperses

Collision!

A moving object rams a stationary object.

Before impact:Kinetic Energy of projectile > 0 Kinetic Energy of target = 0

What happens to the kinetic energy after the collision?

A. All of it goes to the target.B. The projectile and target have equal

kinetic energies.C. The projectile keeps it all.D. It depends; there isn’t enough information

to know for sure.

Group Poll Question

I did the math!

I calculated the kinetic energies of object 1 (projectile) and object 2 (target) as a function of

• Offset• Relative masses

Energy Transfer: Mass Effect

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Offset = 0

KE2

KEtot

m1/M

Energy Transfer: Mass Effect

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Offset = –0.5

KE2

KEtot

m1/M

Energy Transfer: Offset Effect

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

m1/M = 0.5

KE2

KEtot

Offset

Energy Transfer: Offset Effect

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

m1/M = 0.1

KE2

KEtot

Offset

Energy Transfer: Offset Effect

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

m1/M = 0.9

KE2

KEtot

Offset

Collision Summary

• Before impact, all the kinetic energy is in the motion of the projectile.

• At impact, the kinetic energy almost always distributes to motion of both the projectile and target.

• When two objects collide, their kinetic energies are usually closer after the collision than before.

• Spreading out is irreversible.

Kinetic Energy Randomizes

• Spreads out over more objects

• Spreads out in more directions

• Work becomes internal energy

Example

• How does entropy increase when a ball is dropped, bounces, and eventually stops?

• How is energy conserved?• Bouncing ball example applet

www.chem.uci.edu/undergraduate/applets/bounce/bounce.htm

PE KE random molecular KE

Heat Transfer

multiple interactions

Heat Flow

Two solids with different temperatures (average molecular kinetic energies) are brought into contact.

Heat Flow

Two solids with different temperatures (average molecular kinetic energies) are brought into contact. What happens to the atoms’ kinetic energies (temperatures)?

Heat Flow Summary

Molecular kinetic energy flows from high temperature objects to low temperature objects, but not the other way around.This is because kinetic energy tends to even out between colliding objects.

There are more ways to distribute energy among many molecules than among few molecules.

Temperature Difference

HotCold

heat

Until

WarmWarm

Equilibrium

Temperature Difference

HotCold

heat

low SU

high SU

Heat flows until total entropy stops increasing

– Thermal equilibrium– Same temperature

Thermodynamic Temperature

HotCold

heat

low SU

high SU

1/T = S/U

S = q/T

Overall Summary

• Particles and energy tend to become spread out uniformly.

• Entropy is a measure of how many different ways a state can be arranged.

– library analogy

• Total entropy increases in all processes that actually occur.

What It Means

examples

Interesting but vital point

We cannot see most of the motion that occurs in our world.

The Funnel and the Ice Pack

• How can matter ever become localized?– Stars form– Rain falls

• How can thermal motion ever decrease?– Refrigerators and heat pumps– First aid cold packs

• Any time one thing becomes localized, something else spreads out more

Entropy, Technically

• = number of “configurations” of a state

• S = kB ln( = entropy of the state

• S = entropy change– S = S2 − S1

– = kB ln(2) − kB ln(1)

– = kB ln(2/1)

Free Expansion Example

• 2/1 =xVV

N

• S = kN ln(x)

= xN

V

xV

Heat Generation

• Any energy molecular motion– Raises entropy– Energy less constrained

• Effect more important at low temperatures– S = q/T– Greater proportional increase in thermal

energy at low T

Ice Melting Example

• Solid liquid – disperses matter Sc > 0

– constrains energy ST < 0

ST

Sc

0tempS

S

melting temperature

Add Salt

• Salt dissolves in liquid only– Raises S of liquid (+ salt)

– Raises Sc

ST

Sc

0tempS

S

Sc

S

original melting temperature

lower melting temperature

Real Processes

• How can matter ever become localized?– Stars form– Rain falls

• How can temperature ever decrease?– Refrigerators and heat pumps– First aid cold packs

• Whenever one thing becomes localized, something else spreads out more

Group Work

Explain how your process increases entropy. Think about:

• Could the reverse process occur?

• What spreads out: matter, energy or both? How?

• Why does total entropy increase?

Chemical Thermodynamics

• Enthalpy (H) is heat transfer to surroundings

• Spontaneous if G = H – TS < 0

• Equivalent to S – H/T > 0– S is entropy change of system– H/T is entropy change of surroundings

• If a state changes spontaneously, entropy increases.

Entropy and Evolution

• Darwinian evolution is perfectly consistent with thermodynamics.

• Energy from the sun powers life processes.

• Energy from earth radiates into space.

• Material order on earth can increase because energy is dispersed.

• Entropy always increases!

Congratulations!

“[Asking someone to] describe the Second law of thermodynamics is about the scientific equivalent of: Have you read a work of Shakespeare’s?”– C.P. Snow, Rede Lecture, Cambridge, May 7, 1959.