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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