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!
Poll Question
What portion of the time will the molecule
spend in the original volume (left half of the
box)?
a. All
b. Half
c. none
d. 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. All
b. Half
c. 1/3
d. 1/4
Poll Question
What is the probability that the molecule will
be in the original space at any given time?
a. 1
b. 1/2
c. 1/3
d. 1/4
V
V/4
Two Molecules (Poll)
What is the probability that both will be in the
left half of the container at the same time?
a. 1
b. 1/2
c. 1/4
d. 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. 1/2
b. 1/3
c. 1/4
d. 1/8
Whiteboard Work
1. What is the probability that all N will be in
the given sector of the container at the same
time?
xV
V
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
Group Poll Question
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.
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
Offset = 0
1
0.8
0.6
KE2
KEtot
0.4
0.2
0
0
0.2
0.4
0.6
m1/M
0.8
1
Energy Transfer: Mass Effect
Offset = –0.5
1
0.8
0.6
KE2
KEtot
0.4
0.2
0
0
0.2
0.4
0.6
m1/M
0.8
1
Energy Transfer: Offset Effect
m /M = 0.5
1
1
0.8
0.6
KE2
KEtot
0.4
0.2
0
-1
-0.5
0
Offset
0.5
1
Energy Transfer: Offset Effect
m /M = 0.1
1
1
0.8
0.6
KE2
KEtot
0.4
0.2
0
-1
-0.5
0
Offset
0.5
1
Energy Transfer: Offset Effect
m /M = 0.9
1
1
0.8
0.6
KE2
KEtot
0.4
0.2
0
-1
-0.5
0
Offset
0.5
1
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
Hot
heat
Cold
Until
Warm
Equilibrium
Warm
Temperature Difference
Hot
heat
low DS
DU
Cold
high DS
DU
Heat flows until total entropy stops
increasing
– Thermal equilibrium
– Same temperature
Thermodynamic Temperature
Hot
heat
low DS
DU
Cold
high DS
DU
1/T = DS/DU
DS = 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
• W = number of “configurations” of a state
• S = kB ln(W) = entropy of the state
• DS = entropy change
– DS = S2 − S1
–
= kB ln(W2) − kB ln(W1)
–
= kB ln(W2/W1)
Free Expansion Example
•
xV
W2/W1 =
V
•
DS = kN ln(x)
N
= xN
xV
V
Heat Generation
• Any energy  molecular motion
– Raises entropy
– Energy less constrained
• Effect more important at low temperatures
– DS = q/T
– Greater proportional increase in thermal
energy at low T
Ice Melting Example
• Solid  liquid
– disperses matter DSc > 0
– constrains energy DST < 0
DSc
DS
DS 0
DST
melting temperature
temp
Add Salt
• Salt dissolves in liquid only
– Raises S of liquid (+ salt)
– Raises DSc
lower melting temperature
DSc
DSc
DS
DS
DS 0
DST
original melting temperature
temp
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 (DH) is heat transfer to
surroundings
• Spontaneous if DG = DH – TDS < 0
• Equivalent to DS – DH/T > 0
– DS is entropy change of system
– DH/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.