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Entropy (YAC- Ch. 6). In this Chapter, we will: . Introduce the thermodynamic property called Entropy (S) Entropy is defined using the Clausius inequality Introduce the Increase of Entropy Principle which states that

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entropy yac ch 6
Entropy (YAC- Ch. 6)

In this Chapter, we will:

  • Introduce the thermodynamic property called Entropy (S)
  • Entropy is defined using the Clausius inequality
  • Introduce the Increase of Entropy Principle which states that
    • the entropy for an isolated system (or a system plus its surroundings) is always increases or, at best, remains the same.
    • Second Law in terms of Entropy
  • Learn to use the Entropy balance equation: entropy change = entropy transfer + entropy change.
  • Analyze entropy changes in thermodynamic process and learn how to use thermodynamic tables
  • Examine entropy relationships (Tds relations), entropy relations for ideal gases.
  • Property diagrams involving entropy (T-s and h-s diagrams)

Entrpy.ppt, 10/18/01 pages

entropy a property

Entropy is a thermodynamic property; it can be viewed as a measure of disorder. i.e. More disorganized a system the higher its entropy.

  • Defined using Clausius inequality
  • where Q is the differential heat transfer & T is the absolute
  • temperature at the boundary where the heat transfer occurs
Entropy – A Property
  • Clausius inequality is valid for all cycles, reversible and irreversible.
  • Consider a reversible Carnot cycle:
  • Since , i.e. it does not change if you return to the same state,
  • it must be a property, by defintion:
  • Let’s define a thermodynamic property entropy (S), such that

True for a Reversible

Process only

entropy cont d

T

any

process

2

1

reversible

process

S

Since entropy is a thermodynamic property, it has fixed values at a fixed thermodynamic states. Hence, the change, S, is determined by the initial and final state. BUT..

The change is = only for a Reversible Process

Entropy (cont’d)

Consider a cycle, where

Process 2-1 is reversible and 1-2 may or may not be reversible

increase of entropy principle yac ch 6 3
Increase of Entropy Principle (YAC- Ch. 6-3)

Increase of Entropy Principle

Entropy change

Entropy Transfer

(due to heat transfer)

Entropy Generation

The principle states that for an isolated Or a closed adiabatic Or System + Surroundings

A process can only take place such that Sgen 0 where Sge = 0 for a reversible process only

And Sge can never be les than zero.

  • Implications:
  • Entropy, unlike energy, is non-conservative since it is always increasing.
    • The entropy of the universe is continuously increasing, in other words, it is becoming disorganized and is approaching chaotic.
  • The entropy generation is due to the presence of irreversibilities. Therefore, the higher the entropy generation the higher the irreversibilities and, accordingly, the lower the efficiency of a device since a reversible system is the most efficient system.
  • The above is another statement of the second law
second law entropy balance yac ch 6 4

Increase of Entropy Principle is another way of stating the Second Law of Thermodynamics:

    • Second Law : Entropy can be created but NOT destroyed
  • (In contrast, the first law states: Energy is always conserved)
  • Note that this does not mean that the entropy of a system cannot be reduced, it can.
    • However, total entropy of a system + surroundings cannot be reduced
  • Entropy Balance is used to determine the Change in entropy of a system as follows:
    • Entropy change = Entropy Transfer + Entropy Generation where,
  • Entropy change = S = S2 - S1
  • Entropy Transfer = Transfer due to Heat (Q/T) + Entropy flow due to mass flow (misi – mese)
  • Entropy Generation = Sgen 0
  • For a Closed System: S2 - S1 = Qk /Tk + Sgen
  • In Rate Form:dS/dt = Qk /Tk + Sgen
  • For an Open System (Control Volume):
  • Similar to energy and mass conservation, the entropy balance equations can be simplified
  • Under appropriate conditions, e.g. steady state, adiabatic….
Second Law & Entropy Balance (YAC- Ch. 6-4)
entropy generation example

Source

800 K

Q=2000 kJ

Sink

500 K

Entropy Generation Example

Show that heat can not be transferred from the low-temperature sink to the high-temperature source based on the increase of entropy principle.

  • DS(source) = 2000/800 = 2.5 (kJ/K)
  • DS(sink) = -2000/500 = -4 (kJ/K)
  • Sgen= DS(source)+ DS(sink) = -1.5(kJ/K) < 0
  • It is impossible based on the entropy increase principle
  • Sgen0, therefore, the heat can not transfer from low-temp. to high-temp. without external work input
  • If the process is reversed, 2000 kJ of heat is transferred from the source to the sink, Sgen=1.5 (kJ/K) > 0, and the process can occur according to the second law
  • If the sink temperature is increased to 700 K, how about the entropy generation? DS(source) = -2000/800 = -2.5(kJ/K)
  • DS(sink) = 2000/700 = 2.86 (kJ/K)
  • Sgen= DS(source)+ DS(sink) = 0.36 (kJ/K) < 1.5 (kJ/K)
  • Entropy generation is less than when the sink temperature is 500 K, less irreversibility. Heat transfer between objects having large temperature difference generates higher degree of irreversibilities