Engineering Thermodynamics ILecture 31

Spring, 2016

Assoc. Prof., Dr. Yonghua HUANG

http://cc.sjtu.edu.cn

Chapter 6 Using Entropy

Apr/13, Wed, 2016 2

Retrieve property data

p, v, T

u and h

Entropy s

Tables, graphs, equations, software

Reference value

Apr/13, Wed, 2016 3

Reference state for entropy

definition of entropy change

Arbitrarily choosing reference state x, then at any state y,

replace state 1 replace state 2

Only for constant composition applications,for chemical reactions, use absolute values (3rd law)

(Chap. 13)

Because of“cancel”

Apr/13, Wed, 2016 4

Retrieve from table

Table A-2 to A-18 for water and several refrigerants

(superheated) Vapor data: s~f(T, p)

• Example: water, state 1 (3MPa, 500˚C) state 2 (0.3MPa, T2),

s2=s1. T2=?

(sub-cooled) Liquid data: s~f(T, p)

s(T,p)~sf(T)

• Example: water, state 1 (25bar, 200˚C)

A-4

s1=7.2338 kJ/kg·K=s2

A-4interpolating

T2= 183 ˚C

A-5

s1=2.3294 kJ/kg·K

A-2

sf, 200˚C=2.3309 kJ/kg·K

s0.01 ˚C, sat. liq.=0 s-40˚C, sat. liq.=0

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Retrieve from table - cont.

Saturation data: sf, sg

Two-phase data:

• Example: R134a, state 1 (0˚C, u1=138.43kJ/kg)

uf=49.79, ug=227.06

A-10

two-phase

=0.5A-10

Apr/13, Wed, 2016 6

Retrieve from software

IT/EES/Refprop…

Interactive Thermodynamics

Apr/13, Wed, 2016 7

Retrieve from graph

T-s diagram (h, p, v, x) h-s diagram (p, T, x)

steeper

Low p

h(T,p)≈h(T)

Ideal gasMollier diagram

Low p

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Using the Tds equations

A pure, simple compressible system undergoing an

internally reversible process

Neglecting ∆PE, ∆KE

Energy balance:

1st Tds equation:

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Using the Tds equations – cont.

1st Tds equation:

2nd Tds equation:

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Tds equations on unit mass/mole

Unit mass Unit mole

1

2

• Applies to any process, reversible or irreversible

• Between two equilibrium states

Entropy – a property, the equations

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Special case

Apply the Tds equation to a change in phase from

sat. liq. sat. vap. @ const. T and p.

T

ssf sg

0

Const.

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Evaluating ∆s of ideal gas

For ideal gas:

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Using ideal gas table

Defining reference state: s =0 at (T=0K and p=1 atm)

For a state (T, 1 atm)

0

1atm( ,1atm) (0K,1atm) ( ) ln

1atm

T

p

dTs T s c T R

T

0

0

( )( )

T pc Ts T dT

T Specific entropy at T and 1atm: Only f(T), tabulated, A-22,A-23

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Special case: constant cv and cp

Const. cv and cp

∆s:

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∆s of an incompressible substance

Incompressible dv=0

cv = c(T)

du =c(T)dT

1st Tds equation: 0

(liquids, solids)

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Homework:Problems: 6.3, SP1