EGN_3358_Notes_Ch4_First and second laws-Part 2

# EGN_3358_Notes_Ch4_First and second laws-Part 2 - EGN 3358...

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EGN 3358 Thermo-Fluids-Heat Transfer Lecture 7: Systems analysis First and Second Laws of Thermodynamics “Chapter 4 - Part 2” - Entropy

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δ Q T b 0 Clausius Inequality another corollary to the Second Law
Consider Carnot Power Cycle presented in Ch. 5. Process 1-2: Isothermal Exp. Process 2-3: Adiabatic Exp. Process 3-4: Isothermal Compr. Process 4-1: Adiabatic Compr. δ Q T Q T H H = Q T Q T C C = Q T = 0 Q T = 0 Clausius Inequality - Example

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0 = + = C C H H b T Q T Q T Q δ Q Q T T H C H C = Since: Example continued
Consider an Irreversible Heat Engine operating between the same T H and T C as the previous reversible engine. Now: 0 < + = C C H H b T Q T Q T Q δ since we know that Q Q T T H C H C < Clausius Inequality - Example 2

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To make an equation we may write: δ σ Q T b cycle = - The parameter σ may be consider a measure of “strength of the irreversibility” or just “irreversibility”. Irreversibility
Characteristics of Irreversibility If σ cycle = 0 no irreversibilities present within the system, If σ cycle > 0 irreversibilities are present within the system, • If σ cycle < 0 impossible.

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Recall definition of a property: (Any Characteristic of a system, T,P,m,…) Consider cycles shown in Figure Entropy Change
δ σ Q T Q T A C 1 2 2 1 0 + = - = Q T Q T B C 1 2 2 1 0 + = - = 2 1 A B C

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δ Q T Q T A B 1 2 1 2 = Comparing the two equations, observe: Since both path “A” and path “B” are arbitrary except for being internally reversible, the integral δ Q/T has the same value for any internally reversible path from point 1 to point 2. Therefore it has the characteristic of a “property”.
We call this property “Entropy”, (symbol “S”). Entropy is defined in terms of change by: S S Q T rev 2 1 1 2 - = δ int

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Characteristics of Entropy Heat added to system: S > 0 Heat rejected from system: S < 0 Reversible work process: S = 0 Irreversibility in work process: S > 0
Determination of Entropy Phase Change Substance Gas Phase Substance

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Temperature Entropy Temperature - Entropy Diagram
Temperature Entropy Critical Point Saturated Vapor locus Saturated Liquid locus

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Temperature Entropy Critical Point Superheated Vapor region Wet Vapor region Compressed Liquid region
Tabular Values of Entropy Compressed Liquid Saturated Liquid Wet Vapor Saturated Vapor Superheated Vapor

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Process Lines Isothermal Isobaric Isometric Isentropic Isenthalpic Isentergic

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Temperature Entropy Pressure Specific Volume Isothermal
Temperature Entropy Pressure Specific Volume Isobaric

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Temperature Entropy Pressure Specific Volume Isometric
Temperature Entropy Pressure Specific Volume Isentropic

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