Entropy

THIS MEANS THAT THINGS FALL.

THEY FALL FROM HEIGHTS OF ENERGY AND STRUCTURED INFORMATION INTO MATTER IS ENERGY. ENERGY IS INFORMATION.

MEANINGLESS, POWERLESS DISORDER.

EVERYTHING IS INFORMATION.

PHYSICS SAYS THAT STRUCTURES... BUILDINGS, SOCIETIES, IDEOLOGIES...

THIS IS CALLED ENTROPY.

WILL SEEK THEIR POINT OF LEAST ENERGY.

Entropy (S) = a measure of randomness or disorder

Entropy: Time’s Arrow

Entropy: Time’s Arrow

Second Law of Thermodynamics occurs without outside intervention ↓

• In any spontaneous process, the entropy of the universe increases. – ΔSuniverse > 0 • Another version of the 2nd Law:

• Energy spontaneously spreads out if it has no outside resistance • Entropy measures the spontaneous dispersal of energy as a function of temperature – How much energy is spread out – How widely spread out it becomes – Entropy change = “energy dispersed”/T

Entropy of the Universe ΔSuniverse = ΔSsystem + ΔSsurroundings Positional disorder

Energetic disorder

ΔSuniverse > 0 ⇒ spontaneous process Both ΔSsys and ΔSsurr positive

⇒ spontaneous process.

Both ΔSsys and ΔSsurr negative ⇒ nonspontaneous process. ΔSsys negative, ΔSsurr positive

⇒ depends

ΔSsys positive, ΔSsurr negative

⇒ depends

Entropy of the Surroundings (Energetic Disorder)

System

Heat ΔHsys < 0

Entropy

ΔSsurr > 0

Surroundings

Surroundings System

ΔS surr = −

Heat

Entropy

ΔSsurr < 0

ΔHsys > 0

ΔHsys Low T ⇒ large entropy change (surroundings T High T ⇒ small entropy change (surroundings)

Positional Disorder and Probability

Probability of

1

particle in left bulb

=½

"

2

particles both in left bulb = (½)(½) = ¼

"

3

particles all in left bulb

"

4

"

all

"

= (½)(½)(½)(½) = 1/16

"

10

"

all

"

= (½)10 = 1/1024

"

20

"

all

"

= (½)20 = 1/1048576

"

a mole of

"

all

"

= (½)6.02×10

= (½)(½)(½) = 1/8

23

The arrangement with the greatest entropy is the one with the highest probability (most “spread out”).

Entropy of the System: Positional Disorder Ludwig Boltzmann

Ludwig Boltzmann

Ordered states

Low probability (few ways)

Low S

Disordered states

High probability (many ways)

High S

Ssystem ∝ Positional disorder S increases with increasing # of possible positions

Ssolid

< Sliquid <<

Sgas

The Third Law of Thermodynamics

The Third Law: The entropy of a perfect crystal at 0 K is zero. • Everything in its place • No molecular motion

Entropy Curve Solid

Liquid

Gas

← vaporization

S (qrev/T) (J/K)

← fusion

0 0

Temperature (K)

S° (absolute entropy) can be calculated for any substance

Entropy Increases with... • Melting (fusion)

Sliquid > Ssolid

ΔHfusion/Tfusion = ΔSfusion

• Vaporization

Sgas > Sliquid

ΔHvaporization/Tvaporization = ΔSvaporization

• Increasing ngas in a reaction • Heating

ST2 > ST1 if T2 > T1

• Dissolving (usually)

Ssolution > (Ssolvent + Ssolute)

• Molecular complexity

more bonds, more entropy

• Atomic complexity

more e-, protons, neutrons

Recap: Characteristics of Entropy • S is a state function • S is extensive (more stuff, more entropy) • At 0 K, S = 0 (we can know absolute entropy) • S > 0 for elements and compounds in their standard states • ΔS°rxn = ΣnS°products - ΣnS°reactants • Raise T → increase S • Increase ngas → increase S • More complex systems ⇒ larger S