engineering thermodynamics icc.sjtu.edu.cn/g2s/frameworks/ewebeditor/uploadfile/... · 2016. 4....
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Engineering Thermodynamics ILecture 31
Spring, 2016
Assoc. Prof., Dr. Yonghua HUANG
http://cc.sjtu.edu.cn
Chapter 6 Using Entropy
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Apr/13, Wed, 2016 2
Retrieve property data
p, v, T
u and h
Entropy s
Tables, graphs, equations, software
Reference value
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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”
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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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Apr/13, Wed, 2016 5
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
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Apr/13, Wed, 2016 6
Retrieve from software
IT/EES/Refprop…
Interactive Thermodynamics
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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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Apr/13, Wed, 2016 8
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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Apr/13, Wed, 2016 9
Using the Tds equations – cont.
1st Tds equation:
2nd Tds equation:
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Apr/13, Wed, 2016 10
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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Apr/13, Wed, 2016 11
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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Apr/13, Wed, 2016 12
Evaluating ∆s of ideal gas
For ideal gas:
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Apr/13, Wed, 2016 13
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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Apr/13, Wed, 2016 14
Special case: constant cv and cp
Const. cv and cp
∆s:
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Apr/13, Wed, 2016 15
∆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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Apr/13, Wed, 2016 16
Homework:Problems: 6.3, SP1