3.0 The 2nd Law of Thermodynamics

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3.1 Introduction

1st law tells us that for a system undergoing a

change of state, the consequent change in internal

energy of the system, which is dependent only on

the initial and final states, is equal to the algebraic

sum of the heat and work effects i.e.

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It states that a chemical reaction is feasible at

constant T and P if the ΔH is negative.

The law does not explain the magnitudes that q

and w may have and the factors that govern

these magnitudes i.e. it does not explain the

efficiency of converting q into w

Many spontaneous reactions satisfy the above

criterion (i.e. –ve ΔH) , but there are also many

spontaneous reactions that have +ve values of

ΔHrxn !!!

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e.g. CaCO3 decomposes spontaneously at about

900oC into CaO and CO2 absorbing a lot of heat

in the process (endothermic).

In another example, the phase transformation of

tin,

According to the 1st law of the thermodynamics,

grey tin should exist at 25oC

However in reality white tin is found to exist as

the stable form at that temperature

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Therefore the law does not provide a complete

criterion of whether a reaction will occur or not

There is need to define another thermodynamic

property which can provide spontaneity of a given

reaction. This is obtained from 2nd Law

3.2 Spontaneous or Natural

Processes

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For an isolated system (left on its own), either of

the following will occur

o If the system is initially in equilibrium with its

surroundings, it will remain in its equilibrium

state.

o If the initial state is not the equilibrium state,

the system will spontaneously move toward its

equilibrium state.

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A process which involves the self-

generated movement of a system from a

non-equilibrium state to an equilibrium

state is called a natural or spontaneous

process

Determination of the equilibrium state is of

prime importance in thermodynamics, as it

allows us to predict the stability and

direction in which any reaction will

proceed from its initial state

3.3 Reversible and Irreversible

processes

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A process in which the system and surroundings

can be restored to the initial state from the final

state without producing any changes in the

thermodynamics properties of the universe is

called as the reversible process

suppose that the system has undergone change

from state A to state B

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If the system can be restored from state B to

state A, and there is no change in the universe,

then the process is said to be reversible process.

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A reversible process can be reversed completely

leaving no trace left to show that the system had

undergone thermodynamic change

For this to happen there are 2 important

conditions:

o the process should occur in infinitesimally small time

and

o all the initial and final state of the system should be in

equilibrium with each other

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In actual practice the reversible process never

occurs, thus it is an ideal/hypothetical process.

For example;

o Wood will burn spontaneously in air if ignited, but the

reverse process, i.e., the spontaneous recombination

of the combustion products to wood and oxygen in air,

has never been observed in nature!

o Ice at 1 atm pressure and a temperature above 0°C

always melts spontaneously, but water at 1 atm

pressure and a temperature above 0°C never freezes

spontaneously in nature.

o Heat always flows spontaneously from higher to lower

temperature systems, and never the reverse

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These are typical natural processes and

they are irreversible.

Thus for an irreversible process

oThe initial state of the system and surroundings

cannot be restored from the final state

o During the process the various states of the

system on the path of change from initial state

to final state are not in equilibrium with each

other

3.4 Statement of 2nd Law

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The 2nd law has been expressed in various ways.

According to Clausius: No process is possible

whose sole result is the transfer of heat from a

colder body to a hotter body

According to Kelvin and Planck: No process is

possible whose sole result is the complete

conversion of heat into work.

Simply put: spontaneous/natural processes are

not thermodynamically reversible

3.5 Heat and work exchange in

Reversible and Irreversible

Processes

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For a system undergoing a process, let the

maximum work that the system can do be

wmax.

For a reversible process, w = wmax and from

1st law

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However for an irreversible reaction the amount

of work done w, is less than wmax because some

of the energy available to do work is converted

into heat, and the total heat of the system

increases.

i.e. Total heat entering the system (qtot) = heat

entering from surroundings (q) + heat

produced by degradation of work due to

irreversibility (wmax-w) or (qr-q)

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The fact that less heat enters from the

surroundings in the irreversible process than in

the reversible process is due to the heat

produced by the degradation of work in the

irreversible process (e.g. pulley-paddle wheel assembly)

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Therefore an irreversible process is one in

which the system is degraded during the

process.

extent of degradation differs from process to

process.

This suggests that there exists a quantitative

measure of the extent of degradation, or degree

of irreversibility, of a process

3.5 Entropy

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Consider a reversible process in which the

system absorbs an infinitesimal quantity of heat

δq in a reversible manner at a temperature T.

The term δq/T defines the degree of irreversibility

of the process and is called entropy change (ΔS)

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Entropy (S) is an extensive property as it depends

on the mass of the system (its values are additive

just like enthalpy)

It is a thermodynamic property: i.e. depends on the

final state of the system and not on its history!

Entropy is not directly measurable, but entropy

changes are calculated from measurable quantities

such as temperature, pressure, volume and heat

capacity

It represents the degree of “disorderliness” of a

system

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The greater the dispersal of energy or matter in

a system, the higher is its entropy

Adding heat to a material increases the disorder

or entropy of the system.

Unit of S is J/K and that of molar entropy is

J/K.mol.

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In evaluating entropy, it is important to distinguish

between the system and the surroundings.

The total entropy change associated with the process

consists of two terms:

o Entropy change of the system : ΔSsys

o Entropy change of the surroundings : ΔSsurr,

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Recall that the total heat appearing in the system

is the sum of heat entering from the surroundings

(q) and heat produced by degradation due to

irreversibility (qr - q) [eqn 3.1]

We can deduce that the heat of the system

From which

The total heat leaving the surroundings is q . i.e.

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Negative sign indicates that relative to the

surroundings the heat is lost

Thus

combining equations 3.4 and 3.5 into equation

3.3 gives us

i.e.

3.6 Entropy Change for a

Reversible Process

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For a reversible process the sum of entropy

change of the system and the surroundings is

always zero.

Since

It implies

And

Thus

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Total entropy gain of the system is equal to

entropy loss by the surroundings

And for infinitesimal changes,

Simply put: there is no creation or degradation

of entropy; it is only interchanged between

system and surroundings

3.7 Entropy Change for an

Irreversible Process

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For an irreversible (or spontaneous) process, the

sum of entropy change of the system and its

surroundings is always a positive quantity

Since

It implies,

And

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Thus;

Or,

There is a net creation of entropy and this is due

to the degradation of work due to its irreversible

nature.

3.8 Entropy change for a chemical

reaction

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entropy change accompanying a chemical

reaction is defined as the difference between

the sum of the entropies of all products and

the sum of the entropies of all reactants.

Thus for a reaction,

The entropy change;

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Where SM, SN, … are the entropies per mole of

the various substances.

If the reactants and products are in their standard

states, then the entropy change becomes

standard entropy change of reaction

Where SoM, So

N …. refer to the standard molar

entropies of the various substances.

The entropy change of a reaction is generally

evaluated at constant T an P

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Entropy values of elements and compounds are calculated with the help of the 3rd Law of thermodynamics and values at 298K and 1atm are given, just like enthalpy values.

Example 3.1

Calculate the standard entropy change for the reaction

<Cr2O3> + 3<C> = 2<Cr> + 3(CO) at 298K

Given:

So298<Cr2O3> = 81.17 J/K/mol

So298<C> = 5.69 J/K/mol

So298<Cr> = 23.76 J/K/mol

So298(CO) = 197.90 J/K/mol

3.9 Variation of Entropy Change

with Temperature

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If there is change of state of a system such that

the temperature changes, the entropy change

accompanying such a process can be calculated

by integrating between the limit of the

temperature

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Where ST2 and ST1 are the entropies of the

system at temperatures T2 and T1, respectively

And since

It follows that

Or

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The reference entropy is usually that at 298K,

thus

And for substances in their standard state, the

expression becomes;

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In the case of a chemical reaction involving

reactants and products in their standard states,

the changes in standard entropies and heat

capacities must be considered

Eqn 3.11 becomes

If there is any phase transformation taking place

between T1 and T2, then the entropy changes

accompanying such transformations must be

added

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The eqn becomes;

Example 3.2

Zinc melts at 420oC and its standard entropy at

25oC is 41.63 J/K/mol. Calculate the standard

entropy of zinc at 750oC.

Given: ΔHfusion<Zn> = 7.28 kJ/mol

Cp<Zn> = 22.98 + 10.04 x 10-3 T J/K/mol

Cp[Zn] = 21.38 J/K/mol

3.10 Entropy as Criterion for

Equilibrium or Spontaneity

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The entropy function is useful in metallurgical

operations in determining the direction in

which a process will proceed and the final

equilibrium state of the process.

For a chemical reaction proceeding from initial

state A to final state B, then

ΔStotal = ΔSB,total - ΔSA,total

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In an isolated system of constant internal energy

and constant volume,

o If ΔStotal = 0, then the system is at equilibrium

and no spontaneous change will occur

o If ΔStotal > 0, the reaction will occur

spontaneously from sate A to state B

o If ΔStotal < 0, the reaction will occur

spontaneously in the reverse direction i.e.

from state B to state A

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Thus for a chemical reaction within a system will

have positive affinity to take place (or

spontaneous) if it leads to an increase in entropy,

without there being any exchange of heat with the

surroundings.

Most chemical reactions may be carried out

either reversibly or irreversibly, but more heat is

absorbed from the surroundings if the reaction is

carried out in a reversible manner.

3.11 Heat Engines

work can easily be converted to other forms of

energy, but converting heat to work requires the

use of some special devices

A heat engine is a device for converting heat into

work. (e.g., steam engine, internal combustion

engine)

They differ considerably from one another, but all

can be characterized by the following:

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They receive heat from a high-temperature

source (solar energy, oil furnace, nuclear reactor,

etc.)

They convert part of this heat to work (usually in

the form of a rotating shaft)

They reject the remaining waste heat to a low-

temperature sink (the atmosphere, rivers, etc.)

They operate on a cycle.

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The maximum work obtained from the operation of

a heat engine is that generated when all the

processes are reversible i.e. without degradation of

work.

The Carnot cycle (after French Engineer Sadi

Carnot) is the operation of an ideal (reversible)

engine in which heat transferred from a hot

reservoir, is partly converted into work, and partly

discarded to a cold reservoir.

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Work done by the engine for each cycle

w = w1 + w2 - w3 -w4

(w3 and w4 have negative signs because the

system will be contracting)

From 1st law ΔU = q-w = 0 for a cyclic process

and q = q2 – q1 = w

Efficiency of the engine is defined as

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𝜼 = 𝒘𝒐𝒓𝒌 𝒅𝒐𝒏𝒆

𝒉𝒆𝒂𝒕 𝒕𝒂𝒌𝒆𝒏 𝒊𝒏=

𝒘

𝒒𝟐 =

𝒒𝟐 − 𝒒𝟏

𝒒𝟐= 𝟏 −

𝒒𝟏

𝒒𝟐

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Also, the entropy change for each cycle

ΔScycle = ΔS1 + ΔS2 + ΔS3 + ΔS4 = 0

In this case

And therefore

Thus the efficiency depends only on the

temperatures of the reservoirs, and is

independent of the nature of the engine, working

substance, or the type of work performed

𝒒𝟐

𝑻𝟐−

𝒒𝟏

𝑻𝟏= 𝟎

𝜼 = 𝟏 −𝒒𝟏

𝒒𝟐= 𝟏 −

𝑻𝟏

𝑻𝟐

A Carnot engine can be run in reverse and used

to transfer energy as heat from a low

temperature reservoir to a high temperature

reservoir

The device is called a heat pump, if it is used as

a heat source

If it is used to remove heat then it is a

refrigerator

In that case work has to be done on the engine.

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