CHEM 163B THERMODYNAMICS

MIDTERM #2 REVIEWJia Lu (Gabby) jelu@ucsc.eduOffice Hour: Monday 3:00-4:00pm @ PSB 145Gabe Mednick gmednick@ucsc.eduOffice Hour: Wednesday 1:00-2:00pm @ PSB 145

KEY CONCEPTS

• The Second Law of Thermodynamics and Carnot Engine• The Third Law of Thermodynamics and absolute entropy• Clausius inequality• Maxwell’s relation• Gibbs-Helmholtz Equation• Chemical potential and chemical reaction

SECOND LAW OF THERMODYNAMICS

It is impossible for a system to undergo a cyclic process whose sole effects are the flow of heat into the system from a heat reservoir and the performance of an equal amount of work by the system on the surroundings.

CARNOT CYCLE• A combination of 4 reversible processes

• Two isothermal processes• Two adiabatic processes

• Applies to ALL reversible cycles

1

| |1

< 100%

ENTROPY (S)

• Definition of entropy• S= lnΩ• ∆ ≡

• State function – predicts the direction of natural / spontaneous change• ∮ ∮

• Entropy increases (∆ ) for a spontaneous (irreversible process) change in an isolated system

• For reversible processes, ∆ ∆ ∆• For adiabatic processes, q 0 → ∆

ENTROPY DEPENDENCE ON P &V

Constant Pressure

• , → ,• For any system

∆ , κ• For ideal gas

∆ , ln

Constant Volume

• , → ,• For any system

∆ ,

• For ideal gas

∆ , ln

THIRD LAW OF THERMODYNAMICS

The entropy of a pure, perfectly crystalline substance (element or compound) is zero at zero Kelvin.

0 , ′∆ ,

′∆ ,

′

1 0Absolute entropy (in general):•• ↑ as size of molecule increases (↑ DOF)• weakly bound > strongly bound• increases with increasing molar mass

During phase transition

Zero Kelvin can Never be reached

CLAUSIUS INEQUALITY

• From the First Law: • For reversible processes: • Since U is state function,

•• For spontaneous processes

• 0 and 0 (expansion)• 0 and 0 (compression)

• 0• 0 or / > : irreversible processes

= : reversible processes

SPONTANEITY

• Entropy• For an isolated system, ∆

• Helmholtz free energy• Maximum work done on the surroundings• For constant T & V, ∆

• Gibbs free energy• Maximum non-expansion work done on the surroundings• For constant T & P, ∆

Can solely focus on system alone

Need to take into account of surroundings

CHEMICAL MIXTURE(SIMPLE MIXING)

• For real gases and liquids, ∆ 0• For immiscible situations: ∆ 0, ∆ ∆ ∆ 0

• Repulsive interaction• For miscible situations: ∆ 0, ∆ ∆

• Weak repulsive interaction

• For ideal gases, ∆ 0• Ideal gases do not interact with each other• ∆ 0 →• ∆ ∆ 0

DERIVATION OF MAXWELL’S EQUATION

• Knowing:• U = q + w• H = U + PV• A = U - TS• G = H - TS

• Show:•

•

•

•

Hint:

GIBBS-HELMHOLTZ EQUATION

Show ∆

∆

Processinvolvingtwodifferenttemperatures:∆ ∆

∆ ∆∆

1 1

∆

1

∆

1

∆1

1

∆

1At constant P, assuming H

does not depend on T

• Basic mathematic rules•

• If ,• 1 ·

CHEMICAL POTENTIAL

• ≡, ,

• Partial molar Gibbs free energy

• Chemical potential at any states• ° °• ° standard state chemical potential (pure substance, P = 1 bar)

• In multi-components mixtures• ° ∑ °

Standard state pressure = 1 barNormal state pressure = 1 atm

FOR A CHEMICAL REACTION

• ∆ ° ∑ ° ∑ °

• ∆ ° ∑ ,° ∑ ,°

• ∆ ∆ °

•∏ ,∏ ,

Activities (α, unit-less) for:• Gasses

• ° • Solutions

•

• Pure solid or liquid• 1

At equilibrium, NOT °

EQUILIBRIUM CONSTANT (

• At equilibrium,•

• ∆°

• Variations (Le Chatelier’s Principle):• Differential: ∆

°

• Integration: ln ∆°

If • For endothermic reactions

• ∆ ° 0 → ln 0

• Forward reaction spontaneous• →

• For exothermic reactions• ∆ ° 0 → ln 0

• ←