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
Pure Substance
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A substance: a collection of molecules or atoms
A pure substance: A substance that has a homogeneous composition.
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To say something is homogeneous requires us to specify a length scale and a time scale.
A tank of air is homogeneous over a length larger than that between molecules, and
over a time larger than that between collisions.
Below such a length scale and a time scale, the substance is inhomogeneous.
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Liquid-gas mixture
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Phase
One species of molecules can aggregate into several forms, known as phases.
ice
water
steam
Solid
liquid
gas
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System
• A system can be any part of the world.
• The rest of the world is called the surroundings of the system.
weights
Experimental setup: cylinder-piston device
• A fixed number of H2O molecules
• Cylinder, rigid.
• Piston, frictionless.
• Weights
• Fire
vapor
liquid
fire
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Isolated system
• An isolated system does not interact with the rest of the world.
• Seal the cylinder-piston device, so that the number of H2O molecules in the
device is fixed.
• Jam the piston, so that the volume in the device is fixed.
• Insulate the cylinder and the piston, so that the device and the surroundings do
not exchange energy by heat.
• Do whatever necessary to prevent the rest of the world from affecting the system.
weights
vapor
vapor
liquid
liquid
fire
isolated system
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State
• A system isolated for a long time reaches a state of thermodynamic
equilibrium.
• In a state of thermodynamic equilibrium, the system appears to be static at a
macroscopic scale, but molecules keep moving.
• Synonyms: state, state of equilibrium, thermodynamic state, state of
thermodynamic equilibrium.
• The system (a fixed number of H2O molecules) can be in many states.
• Fire and weights transform (change) the system from one state to another.
• The transformation between two states is known as a thermodynamic process.
weights
vapor
vapor
liquid
liquid
fire
isolated system
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Property
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A function of state is called a thermodynamic property (variable).
Examples: temperature, pressure, volume, energy, entropy…
Name all thermodynamic states of a pure substance using two properties, TV
Once the values of the two independent variables are fixed, a state of the
system is fixed.
• Any other property is a function of the two independent variables. P(T,V)
weights
vapor
vapor
liquid
liquid
fire
isolated system
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Intensive and extensive properties
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For a fluid in a state of thermodynamic equilibrium, the
temperature is everywhere the same, and the pressure is
everywhere the same.
Temperature and pressure are intensive properties.
The volume of a system equals the sum of the volumes of all
parts of the system.
Volume is an extensive property.
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Specific volume
volume of system)
(
(specific volume) = mass of system
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)
V
v=
m
(
1
specific volume =
density
)
(
)
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High-school mathematics
Four ways to represent a function of two independent variables, z(x,y)
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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
• A state of coexistent phases: liquid-gas mixture
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Represent states on the T-v plane
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Specify states with two variables, T and v.
Represent a state by a point on the T-v plane.
Pressure is a function, P (T,v)
Represent the function P (T,v) on the T-v plane
by curves of constant pressure (isobaric curves)
weights
vapor
liquid
fire
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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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A state of coexistent phases
Specify a state of coexistent phases by values of two variables (T,v) or (P,v), but not (P,T).
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: (T,x) or (P,x).
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Heat causes giant motion when liquid changes 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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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
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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—system, state, property, and phase
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System: a 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.
Change of phase: 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.
a
P
critical
point
a
liquid
gas
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T
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 the molecular picture of 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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