PPT about the introduction to thermodynamics-entropy-Reference is P K NAG TEXTBOOK

1. Entropy
-ppt-6
Engg Thermodynamics-ME2102
10/13/2023
Presented by,
Lalitha P
Asst. Professor
Mechanical Engg.
RGUKT Basar
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2. Introduction
• Initially first law was stated that for a cycle net HT = net Wt, and
then when TD processes applied on 1st law as the existance of
properties, then the term internal energy was introduced.
• Likewise, for 2nd law also, initially it states in terms of cycles only
and when TD processes applied, 2nd law also leads to new
property definition as entropy.
• First law is said to be the law of internal energy, then 2nd law is
said to be the law of entropy.
• In fact, TD is the study of three E’s, namely,
E  energy
E  entropy and
E  equilibruim.
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3. Two reversible adiabatic paths cannot intersect each other
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5. Clausius Theorem
• Consider a reversible path i-f
• Through the equilibrium point ‘i’ draw on reversible adiabatic line
‘i-a’ and through the point ‘f’ draw another adiabatic line ‘f-b’ and
connect the points ‘a’ and ‘b’ by a reversible isotherm line.
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i
f

6. • Assuming the area under the curve i –f is equal to the area under
the curve i-a-b-f.
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7. • Applying first law on both the processses i=f and i-a-b-f
seperately,
• You get, HT during i-f = HT during i-a-b-f
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8. • i.e., any rev. path may be represented by a reversible zigzag path
(i-aa-bb-f or rev.adiabticrev.isothermrev.adiabatic).
• “Such that the heat transferred during an isothermal process is
the same as that transferred during the original process.”
• Let us consider a smooth closed curve representing a reversible
curve. Divide it is by no.of reversible adiabatic and rev.isothermal
lines as shown in fig.
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• “The cyclic integral of dQ/T for a reversible cycle is zero.”
-Clausius Theorem

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Entropy is the property of system

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• As the entropy is the TD property entropy will be measured at
equilibrium states as,
or
• Entropy is an extensive property of the system. Unit : J/K
• Specific entropy, s = S/m = total entropy /unit mass; unit : J/kg.K

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• For an irreversible process, entropy can be calculated by
converting it to a reversible process since entropy is the point
function.
Entropy-temp. plot
• Pressure versus volume diagram gives the work transfer (WT) for
any process.
• Similarly entropy versus temperature plot is used to calculate the
heat transfer (HT) for any process.

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• i.e., HT can be measured as the product of temperature and
change in entropy.
• The area under the curve on a s-T plot is heat transferred
during the process. It can be calculated reversibly only.

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• Area of the strip (dA) = Tds
• Area of the rev. process i-f (A) =

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• For an isothermal process, T =constant
• For an adiabatic process, dQ = 0 or Tds =0 or S = constant

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Carnot cycle in T-s diagram : 2 rev.isotherms + 2 rev.adiabatics
• Net work o/p = Q1-Q2

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Inequality of Clausius theorem
• Clausius theorem is applicable only rev.process. Then how the
equation must be for irreversible process?

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21. Criterion of the reversibility of a cycle:-
1. If , then the cycle is reversible.
2. If , then the cycle is irreversible and possible
3. If , then the cycle is impossible since it violates the
2nd law.
Entropy change (ds) in an irreversible process
• For any process (natural or practical) undergone by a system,
or
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22. • We know that or for any reversible process.
• So for any irreversible process.
• In general for the total process 1-2, change in entropy can be
written as
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23. Entropy principle
• For an infinitesimal process, …………… (a)
• For an isolated system  no energy transfer ,so dQ = 0 hence
equ. (a) becomes
• For a reversible process, or “s = constant”.
• For an irreversible process, or “s increases”.
• It is thus proved that,
“ the entropy of an isolated system can never decrease. It
always increases (irrev.) and remains constant only (rev.)”.
-principle of increase in entropy or entropy principle
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24. • It is the quantitative general stmt of 2nd law of TD from the
macroscopic view point.
• We know that,
an universe or an isolated s/m = s/m+ surroundings
• For all possible processes that a s/m in the given surroundings
can undergo,
or
• Entropy may decrease locally at some region within the isolated
s/m, but it must be compensated somewhere by greater entropy
increase within the system so that the net effect of an
irrev.process is an entropy increase of the whole s/m.
•
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25. • The entropy increase of an isolated system is a measure of the
extent of irreversibility of the process undergone by the s/m.
• “the entropy of an isolated s/m always increases and becomes a
maximum at the state of equilibrium”.
Rudolf Clausius summerization of 1st and 2nd law of TD
1. The energy of the world (universe) is constant.
2. The entropy of the world tends towards a maximum.
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When the s/m is at equilibrium,
any conceivable change in
entropy would be zero.

26. Entropy and disorder
• Work involves order or the orderly motion of molecules.
• K.E. and P.E. of the molecules of a system gives the orderly
motion of the molecules.
• So work is said to be orderly energy.
• Heat or thermal energy is due to the random thermal motion of
the molecules in a completely disordered fashion and the
avg.velocity is zero.
• Thus, heat is said to be disorderly energy.
• Orderly energy can readily be converted into disorderly energy.
Eg: mechanical energy (into internal energy) into heat.
• But there is natural limitation to convert disorderly energy into
orderly energy.
• Irreversible process always tends to take more disordered
motion-natural tendency. i.e., isolated s/m always tends to
greater entropy ( ).
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27. • So there is a close relation between entropy and disorder.
• So, roughly entropy is defined that,
“ entropy of a system is a measure of the degree of
molecular disorder existing in the system.”
• When heat is imparted to a s/m, disorderly motion of molecules
increases leads to the increase in the entropy of the s/m and
vice versa when heat is removed from the s/m.
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