Entropy

1
Entropy

• Times Arrow

2
Announcements

• Test 2 next Thursday
• covers circular motion through entropy
• closed note, closed book
• One 3 ? 5 card allowed
• Formula sheet provided
• Drill, homework due Tuesday
• Tuesday class review session

3
Objectives

• Explain the tendency of matter and energy to
  spread out over time.
• Identify entropy changes in familiar processes.

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The Flow of Matter

• particles disperse

5
Gas Molecule in a Box

• No energy transfer to walls elastic collisions

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CPS Question

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

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CPS Question

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

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CPS Question

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

V
V/4
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Two Molecules (CPS)

• What is the probability that both will be in the
  left half of the container at the same time?

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Three Molecules (CPS)

• What is the probability that all three will be in
  the left half of the container at the same time?

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Group Work

• What is the probability that all N will be in the
  given quadrant of the container at the same time?

1/4
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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.

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Group It!

• Discuss all succeeding CPS questions with your
  group before answering.

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The Flow of Energy

• energy disperses

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Collision!

• A moving object rams a stationary object.

Before impactKinetic Energy of projectile gt 0
Kinetic Energy of target 0
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CPS Question

• What happens to the kinetic energy after the
  collision?

• All of it goes to the target.
• The projectile and target have equal kinetic
  energies.
• The projectile keeps it all.
• It depends there isnt enough information to
  know for sure.

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• I did the math!

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

• Offset
• Relative masses

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Energy Transfer Mass Effect
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Energy Transfer Mass Effect
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Energy Transfer Offset Effect
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Energy Transfer Offset Effect
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Energy Transfer Offset Effect
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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.

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Kinetic Energy Randomizes

• Spreads out over more objects
• Spreads out in more directions

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Example

• How does entropy increase when a ball is dropped,
  bounces, and eventually stops?
• How is energy conserved?
• Bouncing ball example applet http//itl.chem.ufl.e
  du/4411_f02/applets/bounce/bounce.htm

PE ? KE ? randomized molecular KE
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Heat Transfer

• multiple interactions

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Heat Flow

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

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Heat Flow

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

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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.
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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.

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What It Means

• examples

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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 entropy increase?

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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

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Thermodynamics

• Enthalpy (DH) is heat transfer to surroundings
• Spontaneous if DG DH TDS lt 0
• Equivalent to DS DH/T gt 0
• DS is entropy change of system
• DH/T is entropy change of surroundings
• If something changes spontaneously, entropy
  increases.

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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!

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Congratulations!

• Asking someone to describe the Second law of
  thermodynamics is about the scientific equivalent
  of Have you read a work of Shakespeares?
• C.P. Snow, Rede Lecture, Cambridge, May 7, 1959.