thermodynamics i chapter 2 properties of pure … · thermodynamics i chapter 2 properties of pure...
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Thermodynamics IChapter 2
Properties of Pure Substances
Mohsin Mohd SiesFakulti Kejuruteraan Mekanikal, Universiti Teknologi Malaysia
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Properties of Pure Substances(Motivation)
To quantify the changes in the system, we have to be able to describe the substances which make up the system.
The substance is characterized by its properties.
This chapter shows how this is done for two major behavioral classes of substance covered in this course; phase-change fluids, and gases.
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PURE SUBSTANCE
3 major phases of pure substances;• Solid• Liquid• Gas
• plasma
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Phase Change of Pure Substancesex. Water at 1 atm of pressure
T=25oC
T=100oC
T=100oCSaturated vapor
Saturated liquid
Not about to evaporate
Heat added T
Compressed liquidphase
About to evaporate
Heat added evaporation starts
Saturated liquid phase
Heat added continues evap.
T unchanged
Wet steam or
Saturated liquid-vapor mixture
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Phase Change of Pure Substances
(ctd.)ex. Water at 1 atm of pressure
T=100oC
T=110oC
All liquid evaporated
(about to condense)
Heat removed condensation
Saturated vapor phase
Not about to condense
Heat added T
Superheated vapor phase
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Evaporation temperature changes with pressure
During phase change, temperature and pressure are not independent Tsat <-> Psat
Energy needed to vaporize (latent heat of vaporization) decreases with increasing pressure
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QUALITY, x (2 phase condition)
Saturated liquid-vapor mixture condition
x is a thermodynamic property
x exists only in the liquid-vapor mixture region
mvapor
mliquid
Degree of evaporation
Dryness fraction
qualitymvapor
mtotal
x =
0 x 1
(wet)
100% liquid
(dry)
100% vapor
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Enthalpy of vaporization, hfg (Latent heat of vaporization): The amount of energy needed to vaporize a unit mass of saturated liquid at a given temperature or pressure.
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Quality (cont.)
𝑥 =𝑚𝑔
𝑚𝑔 + 𝑚𝑓1 − 𝑥 =
𝑚𝑓
𝑚𝑔 + 𝑚𝑓
𝑥 ≡𝑚𝑔
𝑚𝑔 + 𝑚𝑓
=𝑣 − 𝑣𝑓
𝑣𝑔 − 𝑣𝑓=
ℎ − ℎ𝑓
ℎ𝑔 − ℎ𝑓
=𝑢 − 𝑢𝑓
𝑢𝑔 − 𝑢𝑓=
𝑠 − 𝑠𝑓
𝑠𝑔 − 𝑠𝑓
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Some Additional Thermodynamic Properties
Internal Energy, U [kJ]Specific Internal Energy, u [kJ/kg]
Enthalpy, H [kJ]
H ≡ U + PV
Specific Enthalpy, h [kJ/kg]
h = u + Pv
Entropy, S [kJ/K]Specific Entropy, s [kJ/kg.K]
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PROPERTY TABLES
3 types of tables
Compressed liquid table
Saturated table
Superheated table
Saturated tables
Temperature table – T in easy to read numbers
Pressure table – P in easy to read numbers
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Compressed Liquid Approximation
Because liquid is more sensitive to changes of temperature than that of pressure
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Choosing which table to use
Determine state (phase) first!
How? Compare the given properties against the saturated table
(ex. given h & T)
If hf ≤ h ≤ hg at the given T
→Mixture phase
→ use saturated table
If h > hg at the given T
→ Superheated phase
→ use superheated table
If h < hf at the given T
→ Compressed liquid phase
→ use saturated table
ℎ ≈ ℎ𝑓𝑇
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Choice of tables (cont.)
If P & T is given
P ↔ Tsat
T ↔ Psat
P > Psat at the given T
T < Tsat at the given P
P < Psat at the given T
T > Tsat at the given P
Compressed liquid
Superheated vapor
Best determined by simple sketching of the p-v or T-v diagram
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Choice of tables (additional)
(ex. given h & P)
If hf ≤ h ≤ hg at the given P
→Mixture phase
→ use saturated table
If h > hg at the given P
→ Superheated vapor phase
→ use superheated vapor table
If h < hf at the given P
→ Compressed liquid phase
→ use saturated table
P ↔ Tsatℎ ≠ ℎ𝑓
𝑃
ℎ ≈ ℎ𝑓𝑇𝑠𝑎𝑡
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Notes on Using Property Tables
Some tables do not list h (or u)→ u (or h) can be obtained from h = u + Pv
Values for compressed liquid is taken as the
same as that of saturated liquid at the same
temperature
ex. T=25oC, P=1 bar (compressed liquid)
h25C,1b ≈ hf@T=25C
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Interpolation (Linear Interpolation)
T
Ta
Tb
va v=? vb
Assume a & b
connected by a straight linea
b
Employ concept of slope ∆𝑦
∆𝑥= constant
∆𝑣
∆𝑇=
𝑣 − 𝑣𝑎
𝑇 − 𝑇𝑎=
𝑣𝑏 − 𝑣𝑎
𝑇𝑏 − 𝑇𝑎
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Ideal Gas (Initial Observations)
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IDEAL GAS(for pressures much lower than critical pressure)
Equation of state for ideal gas
R = Gas Constant [kJ/kg.K](constant for a gas, value
depends on type of gas)
𝑅 =𝑅𝑢
𝑀
𝑅𝑢 = Universal Gas Constant = 8.314𝑘𝐽
𝑘𝑚𝑜𝑙. 𝐾
𝑅 =𝑃1𝑉1
𝑇1𝑚1=
𝑃2𝑉2
𝑇2𝑚2
𝑀 = Molecular mass𝑘𝑔
𝑘𝑚𝑜𝑙
Can be used to relate between
different states
𝑃𝑉
𝑚= 𝑅𝑇 𝑃𝑣 = 𝑅𝑇
𝑃𝑉 = 𝑚𝑅𝑇
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Ideal gas u, h, cp, cv relationship
Constant Volume Specific Heat Capacity cv
Constant Pressure Specific Heat Capacity, cp
𝑐𝑣 =𝑑𝑢
𝑑𝑇
𝑐𝑝 =𝑑ℎ
𝑑𝑇
𝑑𝑢 = 𝑐𝑣𝑑𝑇
𝑑ℎ = 𝑐𝑝𝑑𝑇
𝑐𝑝 = 𝑐𝑣 + 𝑅
𝑐𝑝
𝑐𝑣= 𝑘 = specific heat ratio
𝑐𝑝 =𝑘𝑅
𝑘 − 1
𝑐𝑣 =𝑅
𝑘 − 1
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POLYTROPIC PROCESS
-Processes that obey/follow the pathpvn = c
n = polytropic index
p
v
pvn = c
p1v1n = p2v2
n
1
2
−∞ ≤ 𝑛 ≤ ∞
Can be used to relate between two states
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n = 1 isothermaln = 0 isobaricn = const. volume
Some special cases for polytropic processes
Ideal Gas & Polytropic Process combined
1
2
1
1
1
2
1
2
nn
n
v
v
p
p
T
T
±∞
Can be used to relate between two states
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Real Gases & Compressibility Factor
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Compressibility Factor
𝑍 =𝑃𝑣
𝑅𝑇=
𝑣
𝑅𝑇𝑃
=𝑣actual𝑣ideal
𝑇𝑅 =𝑇
𝑇cr
𝑃𝑅 =𝑃
𝑃cr
𝑣𝑅 =𝑣𝑎𝑐𝑡𝑢𝑎𝑙
𝑅𝑇𝑐𝑟
𝑃𝑐𝑟Reduced pressure
Reduced temperature
Pseudo-reduced specific volume
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H2O (Water, Steam)
Property Tables !!!
Ideal Gas
pV = mRT& other relationsh = cpTu = cvTetc.
Air,N2 , He, etc.
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Other Equations of State
Van der Waal’s :
Beattie-Bridgeman :
Benedict-Webb-Rubin :
𝑝 +𝑎
𝑣2𝑣 − 𝑏 = 𝑅𝑇
𝑃 =𝑅𝑢𝑇
𝑣21 −
𝑐
𝑣𝑇3 𝑣 + 𝐵 −
𝐴
𝑣2
Virial equations of state:
𝑃 =𝑅𝑇
𝑣+
𝑎(𝑇)
𝑣2+
𝑏(𝑇)
𝑣3+
𝑐(𝑇)
𝑣4+ ⋯
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The apparent and the implied
Some examples…
Constant volume (V=c)
Constant pressure (p=c)
Rigid tank
Frictionless cylinder, freely moving piston
The ImpliedThe Apparent