Properties, states and phases
of a pure substance
I am teaching Engineering Thermodynamics using the textbook by Cengel and Boles.
Many figures in the slides are taken from that book, and most others are found online.
Similar figures can be found in many places.
I went through these slides in two lectures, each 90 minutes.
Zhigang Suo
Thermodynamics relates heat and motion
thermo = heat
dynamics = motion
Pure Substance
A substance: a collection of molecules or atoms
A pure substance: A substance that has the same composition everywhere.
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Liquid-gas mixture
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Phases
One species of molecules can aggregate into several forms, known as phases.
ice
water
steam
Solid
liquid
gas
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actions and words
Parts of an experimental setup
•A fixed number of H2O molecules
•Cylinder
•Frictionless, perfectly sealed piston
•Weights
•Fire
System
•A fixed number of H2O molecules
The system interacts with the surroundings
•Weights transfer energy to the system by work.
•Fire transfers energy to the system by heat.
Thermodynamic variables (properties) of the system
•Temperature, pressure, volume, energy, entropy…
Thermodynamic states of the system
•The system approaches a thermodynamic state of equilibrium.
•The states of the system has two independent variations.
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A bit of high-school mathematics
Four ways to represent
a function of two variables, f(x,y)
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•
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Contour plot (plane diagram)
Table
A surface in 3D
An equation
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compressed
liquid
saturated
liquid
coexistent
Liquid and vapor
saturated
vapor
superheated
vapor
a
States
• Specify states with two variables, T and V
• Change of state
• Continuous change of state
Phases
• Two phases: liquid and gas
• Change of phase
• Discontinuous change of state
• Co-existent phases: liquid-gas mixture
• A state of coexistent phases
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Represent states on TV
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•
•
•
Specify states with two variables
A point on the TV plane represents a state
Pressure is a function, P (T ,V)
Curves of constant pressure
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The discovery of the dome
A point inside the dome specifies a state of coexistent phases.
Thomas Andrews, On the continuity of the gaseous and liquid states of matter.
Philosophical Transactions of the Royal Society of London 159, 575-590 (1869)
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Two paths to change from one state to another state
A path of continuous change of state
A path of discontinuous change of state
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Heat causes giant motion when liquid turns to gas
P = 100 kPa
Tsat = 100 degC
Vf = 10-3 m3/kg
Vg = 1.7 m3/kg
https://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter2a.html
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Represent states on PV
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https://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter2a.html
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Saturation Temperature and Saturation Pressure
liquid
gas
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Two paths
to change from one state to another state
A path of discontinuous change of state
A path of continuous change of state
a
a
P
P
critical
point
critical
point
liquid
a
a
liquid
gas
gas
T
a
T
a
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Pressure cooker
Invented by Denis Papin, France, 1679
Invention: increase pressure, increase temperature, reduce cooking time.
Science: When water and steam coexist, temperature increases with time.
Engineering: seal, strength, control pressure or temperature.
P ~ 2 atm
T ~ 120 dedC
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Bottled gas by liquefaction
Invention: store gas in small volume, at room temperature .
Science: At room temperature and high pressure, some gases become liquids.
Engineering: seal, strength. No need for thermal insulation.
Ammonia, NH3
liquid
gas
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Fix temperature by using boiling point
Invention: Fix temperature by using boiling points of various liquids.
Science: When a liquid evaporates at the atmospheric pressure, the temperature is fixed.
Engineering: seal, insulation.
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Specify a state of coexistent phases
Specify a state of coexistent phases by values of two variables: Tv or Pv, but not PT.
Define quality by
x=
mgas
mgas + mliq
T
0 < x < 1: a mixture of liquid and vapor
x = 0: saturated liquid
x = 1: saturated vapor
v
vf
Volume and specific volume
(
v
vg
vf specific volume of saturated liquid
vg specific volume of saturated gas
v specific volume of a mixture of liquid and gas
)
V = mgas + mliq v, Vliq = mliqv f , Vgas = mgasvg
Volume is additive V = Vliq +Vgas
(
)
Specific volume follows rule of mixture v = 1 - x v + xv
f
g
Two more ways to specify a state of coexistent phases: Tx or Px.
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Tables of properties inside the dome
coexistent liquid and vapor
A partial list of Table A–4.
• Table A–4: Saturation properties of
water under temperature.
• Table A–5: Saturation properties of
water under pressure.
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Tables of properties outside the dome
Compressed liquid or superheated vapor
Specify a state by values of PT
A partial listing of Table A–6.
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A bit of high-school science
Ideal-gas law
PV = RT
Equation of state: An equation that relates properties of a substance.
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Is Water Vapor an Ideal Gas?
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Principle of corresponding states
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Use PT as independent variables.
Normalize them by critical vales.
Any property is a function of the two independent variables.
Pv/RT is a (dimensionless) property.
æ P T ö
Pv
÷÷
= f çç
,
RT
è Pcr Tcr ø
TR = T /Tcr
Pv
RT
•
•
•
•
P / Pcr
At low pressure, and all temperatures, all substances approach to ideal gas, Pv/RT ~ 1.
At high temperature, and all pressures, all substances approach to ideal gas, Pv/RT ~ 1.
Any property is a function of the two independent variables.
The function Pv/RT = f(P/Pcr, T/Tcr) is nearly the same for all substances.
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van der Waals Equation of State
Critical isotherm of a pure substance has an
inflection point at the critical point.
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Summary—states, properties, and phases
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•
•
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•
•
One pure substance of a fixed number of molecules: H2O.
Two phases: liquid and gas.
Many (thermodynamic) states, specified by two independent thermodynamic variables (properties).
T,V as independent variables. Curves of constant P represent function P(T,V). A point on the left of the dome
represents a state of liquid, a point on the right of the dome represents a state of gas, and a point under the
dome represents a state of coexistent phases.
P,V as independent variables. Curves of constant T represent function T(P,V).
P,T as independent variables. Many states of coexistent phases fall on the same point on the phase boundary.
A change of phase: a discontinuous change of state.
A single state is represented by three points on three planes.
The states of coexistent phases are represented by the regions under the domes on the T-V plane and P-V
plane, and by the phase boundary on the P-T plane.
P and T are intensive properties. V is an extensive property.
liquid
gas
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Three phases
Triple point
liquid
sublimation/cond
ensation
melting/freezing
evaporation/cond
ensation
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https://en.wikipedia.org/wiki/Water_(data_page)
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Liquid water is denser than ice
The crystalline structure of ice is very open.
Liquid water packs tighter.
Ice floats on top of water
http://chemistry.elmhurst.edu/vchembook/122Adensityice.html
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http://www.wardteam.com/Blog/Preventing-Frozen-Pipes
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https://commons.wikimedia.org/wiki/File:Phase_diagram_of_water.svg
Phase diagram unlike that of water
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The function P(T,V)
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Project a surface in 3D to planes
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Borgnakke and Sonntag, Fundamentals of Thermodynamics
Project a surface in 3D to planes
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Borgnakke and Sonntag, Fundamentals of Thermodynamics
Phase diagram on P-V plane
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Questions that motivate later lectures
1.
2.
3.
4.
5.
What is temperature?
What is a thermodynamic state?
Why does a system isolated for a long time reach equilibrium?
What is equilibrium?
Once in equilibrium, the isolated system will never get out of
equilibrium. Why?
6. The phase diagrams of many pure substances look similar (i.e., coexistent phases, triple point, critical point). Why?
7. Beside TVP, what are other thermodynamic properties?
8. How do we use diagrams and tables of properties to design
engines?
9. How do we invent new devices?
10. How about impure substances, such as air and saltwater?
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