Chapter 7 Slides modelling subject

8/18/2019 Chapter 7 Slides modelling subject

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1/48© U N I V E R S I T I T E N A G A N A S I O N A L , 2 0 1 5

M E H B 2 1 3 T H E R M O D Y N A M I C S 1 : C H A P T E R 7

CHAPTER 7

ENTROPY

Prepared by:

Saiful Hasmady Abu Hassan, Dr.

Adapted from:

Yunus A. Cengel and Michael A. Boles, Thermodynamics: AnEngineering Approach, 8th Edition in SI Units, McGraw-Hill, 2015



Chapter 7 Outcomes

At the end of the chapter, you should be able to:

• Apply the second law of thermodynamics to processes

• Define a new property called entropy to quantify the second-law

effects

• Establish the increase of entropy principle

• Calculate the entropy changes that take place during processes for

pure substances, incompressible substances, and ideal gases

• Examine a special class of idealized processes, called isentropic

processes, and develop the property relations for these processes

• Derive the reversible steady-flow work relations

• Develop the isentropic efficiencies for various steady-flow devices

• Introduce and apply the entropy balance to various systems


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Entropy

Clausius Inequality

Reversible, irreversible

Internally reversible

Formal Definition of Entropy

[kJ/K]



EntropyEntropy Change of Internally Reversible Heat

Transfer Process

Entropy change of thermal

energy reservoirs


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The Increase of Entropy Principle

From Clausius Inequality,

To make the ‘>’ sign becomes ‘=‘,

?



Sgen: Entropy Generation

• Some entropy is generated or created during

an irreversible process, and this generation is

due entirely to the presence of irreversibilities

• The entropy generation Sgen is always a

positive quantity or zero


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Sgen: Isolated Systems



Some Remarks about Entropy1. Processes can occur in a certain direction

only, not in any direction• A process must proceed in the direction of

increasing entropy (Sgen ≥ 0)

• A process that violates this principle isimpossible

2. Entropy is a non-conserved property , andthere is no such thing as the conservationof entropy principle

• Entropy is conserved during the idealizedreversible processes only

• Entropy increases during all actualprocesses

3. Entropy generation is a measure of themagnitudes of the irreversibilities duringthat process• Sgen is a measure of performance

degradation of engineering devices


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Entropy Change of Pure Substances

The T-s Diagram (for

water)

[kJ/K]



Isentropic Processes

[kJ/(kgK)]

!


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Property Diagrams Involving Entropy

• On a T-S diagram, the areaunder the process curverepresents the heat transferfor internally reversibleprocesses

1. The T-s (or T-S) Diagram

For internally reversible,

isothermal process:



Property Diagrams Involving Entropy1. The T-s (or T-S) Diagram


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Property Diagrams Involving Entropy

2. The h-s (or Mollier ) Diagram



What is Entropy?

A pure crystalline substance at absolute

zero temperature is in perfect order, and

its entropy is zero (the third law of

thermodynamics)


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What is Entropy?



What is Entropy?


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The T dS RelationsWhy? To determine the entropy change Δs of solids, liquids and ideal gases

Since and

Substituting and rearranging,

Per unit mass,

The First T ds Relation (Gibbs Equation)



The T dS Relations

The Second T ds Relation

From the enthalpy definition,

Applying Chain Rule to the above,

And knowing the First T ds Relation to be

Why? To determine the entropy change Δs of solids, liquids and ideal gases


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The T dS Relations

• Differential changes in entropy in terms of other properties

• Will be used to find Δs of solids and liquids, and ideal gases

Why? To determine the entropy change Δs of solids, liquids and ideal gases



Entropy Change of Liquids and Solids

From the First T ds Relation,

Liquids and solids can be approximated as incompressible substances since

their specific volumes remain nearly constant during a process. Thus:

Knowing that and for solids and liquids,

LIQUIDS AND SOLIDS:

For isentropic process of an

incompressible substance:


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Entropy Change of Ideal Gases1. From the First T ds Relation

Knowing

and

2. From the Second T ds Relation

Knowing

and

The TWO equations above can be used for IDEAL GASES. However, the INTEGRAL sign remains.

IDEAL GASES #1: IDEAL GASES #2:



Entropy Change of Ideal Gases

• To ‘remove’ the integral, entropy change of

ideal gases can be found from two kinds of

analyses:

1. Approximate Analysis (or the Constant Specific

Heat Method)

2. Exact Analysis (or the Variable Specific HeatMethod)


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Entropy Change of Ideal Gases1. APPROXIMATE ANALYSIS (CONSTANT SPECIFIC HEAT METHOD)



Entropy Change of Ideal Gases1. APPROXIMATE ANALYSIS (CONSTANT SPECIFIC HEAT METHOD)

Summary: Entropy change of an ideal gas on a unit –mass basis [kJ/(kgK)]

Summary: Entropy change of an ideal gas on a unit –mole basis [kJ/(kmolK)]


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Entropy Change of Ideal Gases2. EXACT ANALYSIS (VARIABLE SPECIFIC HEAT METHOD)

We choose absolute zero as the reference

temperature and define a function s° as

Therefore

From the Second T ds Relation,



Entropy Change of Ideal Gases


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Isentropic Processes of Ideal Gases

•

Similar to entropy change, the propertiesduring isentropic processes of ideal gases can

be numerically related from the two analyses:

1. Approximate Analysis (or the Constant Specific

Heat Method)

2. Exact Analysis (or the Variable Specific Heat

Method)

•

s2 – s1 = 0 is set



Isentropic Processes of Ideal Gases1. APPROXIMATE ANALYSIS (CONSTANT SPECIFIC HEAT METHOD)

Rearranging, we arrive at three relations:

For isentropic, ideal gas and constant specific heats


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Isentropic Processes of Ideal Gases2. EXACT ANALYSIS (VARIABLE SPECIFIC HEAT METHOD)

Isentropically,

Which leads to

Rearranging,

For isentropic, ideal gas, and variable specific heats,

(relative pressure)

(relative specific volume)



Isentropic Processes of Ideal Gases2. EXACT ANALYSIS (VARIABLE SPECIFIC HEAT METHOD)

For isentropic, ideal gas, and variable specific heats,


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Reversible Steady-flow Work

Energy balance:

Since

Substituting and rearranging,

Reversible Work:

(in the absence of KE and PE)

Therefore,

(constant v )



Reversible Steady-flow WorkEXAMPLE: Compressing a Substance in

the Liquid versus Gas Phases


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Isentropic Efficiencies of Steady-flow Devices

1. ISENTROPIC EFFICIENCY OF TURBINES



Isentropic Efficiencies of Steady-flow Devices1. ISENTROPIC EFFICIENCY OF TURBINES


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2. ISENTROPIC EFFICIENCY OF COMPRESSORS AND PUMPS

Compressors

Pumps

Compressors are

sometimesintentionally cooled

to minimize the work

input



Isentropic Efficiencies of Steady-flow Devices2. ISENTROPIC EFFICIENCY OF COMPRESSORS AND PUMPS

Compressors


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3. ISENTROPIC EFFICIENCY OF NOZZLES

If the inlet velocity of the fluid is small relative

to the exit velocity, the energy balance is



Isentropic Efficiencies of Steady-flow Devices3. ISENTROPIC EFFICIENCY OF NOZZLES


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Entropy Balance



Entropy BalanceMECHANISMS OF ENTROPY TRANSFER, Sin and Sout

1. HEAT TRANSFER

(T = constant)

By the way,


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Entropy BalanceMECHANISMS OF ENTROPY TRANSFER, Sin and Sout

2. MASS FLOW



Entropy BalanceENTROPY GENERATION, Sgen


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Entropy Balance

The entropy of a substance always increases

(or remains constant in the case of a reversibleprocess) as it flows through a single-stream,

adiabatic, steady-flow device



Entropy BalanceEntropy balance for heat transfer

through a wall

Entropy balance for a throttling process


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Entropy BalanceEntropy Generated when a Hot Block Is Dropped in a Lake

or

Entropy Generation in a Heat Exchanger



Entropy Balance

Entropy Generation Associated with

Heat Transfer


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Entropy Balance

Entropy generation associated with a heat transfer process



What we covered

• Entropy• The Increase of entropy principle• Entropy change of pure substances• Isentropic processes• Property diagrams involving entropy• What is entropy?• The T ds relations

• Entropy change of liquids and solids• The entropy change of ideal gases• Reversible steady-flow work• Minimizing the compressor work• Isentropic efficiencies of steady-flow devices• Entropy balance

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Chapter 7 Slides modelling subject