Chapter 3: The Second Law of Thermodynamics

• Spontaneous Processes• Entropy• The Carnot Heat Engine• The Second Law of Thermodynamics• The Third Law of Thermodynamics• Gibbs Free Energy• Gibbs and Helmholtz Energies and its

Applications

First Law vs Second Law

The First Law of Thermodynamics - Energy can change from one form to another but cannot be destroyed or created- Internal energy and enthalpy of a reaction(1st law of thermodynamics cannot explain the direction of the process)

The Second Law of Thermodynamics- Chemical processes tend to favor one direction

Spontaneous Process

• In terms of chemical reaction:- We consider exothermic and endothermic

reactions,- “exothermic reaction seems to favor

spontaneity while endothermic reaction is not”

• Some spontaneous process (conversion of diamond to graphite) maybe so slow that the tendency never realized in practice.

• Thus, in order to determine the spontaneity of a reaction, we need another term called ENTROPY (S)

• A reaction that does occur in a given set of conditions – spontaneous reaction

• A reaction that does not occur under specified conditions – non-spontaneous reaction– Examples:

A waterfall runs downhill but never up, spontaneouslyWater freezes below 0°C and ice melts above 0°C, spontaneously (at 1 atm)Heat flows from hotter object to colder one, but reverse never happens spontaneouslyIron exposed to water and oxygen forms rust, but rust does not change back to iron spontaneously

Spontaneous Process

What determines reaction of spontaneous

change?

The Dispersal of Energy• Ball does not rise as high after

each bounce due inelastic losses. • Kinetic energy of the ball’s overall

motion (energy of thermal motion of its particles and those of the floor that it hits).

• Direction of spontaneous change: toward a state in which a ball at rest with all its energy dispersed into random thermal motion of molecules and of the atoms of the virtually infinite floor.

Ball (system) bouncing on a floor (surrounding).

• An object does not spontaneously become warmer than its surroundings. It is impossible that the jostling of randomly vibrating atoms in the surrounding will lead to the localization of thermal motion in the object.

• Opposite change: the spreading of the object’s energy into the surroundings as thermal motion is natural.

Entropy is often described as a measure on how disperse or spread out the energy of a system among the different possible ways that a system can contain energy

The GREATER the dispersal of energy the GREATER the entropy of a system

A system that spread to lower microstates has lower entropy

A system that spread to higher microstates has higher entropy

Entropy, S

Consider a cup of hot coffee:Has a certain amount of entropy due to the dispersal among the various energy states of water molecules (vibrate, rotate,etc.)Various energy states/dispersal of energy known as MICROSTATES

> microstates , > entropyMicrostates increase with temperature (i.e. more vibration and more rotation of

molecules)

Spontaneous Process

Spontaneous Process

Entropy and Microstates

Second Law and Entropy

• Focus on the change of entropy, dS that occurs as a result of ‘process’ change

• The thermodynamic definition of entropy is based on expression

• For a measurable change between to states i and f,

• Thus, to calculate the difference in entropy between any two states of a system, find reversible path between them, integrate the energy supplied as heat at each stage of the path divided by the temperature at which heating occurs.

Thermodynamic definition of entropy

T

dqdS rev

T

dqS revf

i

Example:

Calculate the entropy change of a sample of perfect gas when it expands isothermally from a volume Vi to a volume Vf.

Since T is constant, thus

Surroundings

Example:

Second Law Thermodynamics

Second Law Thermodynamics

Carnot heat engine/Carnot cycle

Efficiency () = work performed = l w l

heat adsorbed qh

This shows the greater the work output for a given supply of heat from the hot reservoir, the GREATER is the EFFICIENCY of the engine.

Since the energy supplied as work by the engine is not same to energy supplied as heat by the hot reservoir and returned to the cold reservoir, the efficiency can be expresses in terms of heat transaction alone,

= qh + qc = 1 + qc for qc < 0, rev = 1 - Tc

qh qh Th

Efficiency of a heat engine

• From expression, The Second Law of thermodynamics implies that all reversible engines have the same efficiency regardless of their construction (the relation between heat transfer and temperature is independent of the working material and true for any substance involves in Carnot Cycle.

The Third Law Thermodynamics

The Third Law

Third Law Thermodynamics

Third Law Thermodynamics

Entropy change

Entropy changes for specific process

• Phase transition– The degree of dispersal of matter and energy

changes when a substance freezes or boils • As a result of changes in the order with which the molecules

pack together and the extent to which the energy is localized or dispersed

– The transition is accompanied by a change in entropy

– Consider a system and its surrounding at normal transition temperature, Ttrs (the T at which 2 phases are in equilibrium at 1 atm)

Entropy changes for specific process

• Tice (s)(0oC, 1atm) Twater(l)(0oC, 1atm)• Twater(l)(100oC, 1atm) Tvapour(g)(100oC, 1atm)

– At Ttrs, any transfer of energy as heat between the system and its surrounding is reversible because the two phases are reversible

• Therefore, the change in molar entropy of the system is – trsS = trsH/Ttrs, at constant pressure q=trsH– trsH < 0, the phase transition is exothermic;

Freezing and condensation– trsH > 0 the phase transition is endothermic; Melting and vaporisation

Entropy changes for specific process

Entropy changes for specific process

Gibbs Energy

Gibbs Energy