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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. True. False. The Flow of Matter. particles disperse. Gas Molecule in a Box.

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entropy

Entropy

Time’s Arrow

objectives
Objectives
  • Explain the tendency of matter and energy to spread out over time.
  • Identify entropy changes in familiar processes.
poll question
Poll Question

I think I know what “entropy” means.

  • True.
  • False.
the flow of matter

The Flow of Matter

particles disperse

gas molecule in a box
Gas Molecule in a Box

No energy transfer to walls: elastic collisions

gas molecule in a box6
Gas Molecule in a Box

Double the size of the box!

gas molecule in a box7
Gas Molecule in a Box

Double the size of the box!

poll question8
a. Allb. Half

c. noned. 75%

Poll Question

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

poll question9
Poll Question

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

poll question10
a. Allb. Half

c. 1/3d. 1/4

Poll Question

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

poll question11
a. 1b. 1/2

c. 1/3d. 1/4

Poll Question

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

V

V/4

two molecules poll
a. 1b. 1/2

c. 1/4d. 0

Two Molecules (Poll)

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

three molecules poll
a. 1/2b. 1/3

c. 1/4d. 1/8

Three Molecules (Poll)

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

whiteboard work
Whiteboard Work
  • What is the probability that all N will be in the given sector of the container at the same time?

xV

V

expansion summary
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
Group It!

Discuss all succeeding poll questions with your group before answering.

the flow of energy

The Flow of Energy

energy disperses

collision
Collision!

A moving object rams a stationary object.

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

group poll question
Group Poll 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 isn’t enough information to know for sure.
slide20
I did the math!

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

  • Offset
  • Relative masses
collision summary
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
Kinetic Energy Randomizes
  • Spreads out over more objects
  • Spreads out in more directions
  • Work becomes internal energy
example
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

Heat Transfer

multiple interactions

heat flow
Heat Flow

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

heat flow31
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
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
Temperature Difference

Hot

Cold

heat

Until

Warm

Warm

Equilibrium

temperature difference34
Temperature Difference

Hot

Heat flows until total entropy stops increasing

  • Thermal equilibrium
  • Same temperature

Cold

heat

DS

DS

high

low

DU

DU

thermodynamic temperature
Thermodynamic Temperature

Hot

1/T = DS/DU

DS = q/T

Cold

heat

DS

DS

high

low

DU

DU

overall summary
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.
    • libraryanalogy
  • Total entropy increases in all processes that actually occur.
interesting but vital point
Interesting but vital point

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

the funnel and the ice pack
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
Entropy, Technically
  • W = number of “configurations” of a state
  • S = kBln(W) = entropy of the state
  • DS = entropy change
    • DS = S2− S1
    • = kBln(W2) − kBln(W1)
    • = kBln(W2/W1)
free expansion example
Free Expansion Example
  • W2/W1 =

= xN

N

xV

V

  • DS = kNln(x)

xV

V

heat generation
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
Ice Melting Example
  • Solid  liquid
    • disperses matter DSc > 0
    • constrains energy DST < 0

DSc

DS

DS

0

temp

DST

melting temperature

add salt
Add Salt
  • Salt dissolves in liquid only
    • Raises S of liquid (+ salt)
    • Raises DSc

lower melting temperature

DSc

DSc

DS

DS

DS

0

temp

DST

original melting temperature

real processes
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
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
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
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

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.

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