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

A substance: a collection of molecules or atomsA pure substance: A substance that has the same composition everywhere.

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Pure Substance

Liquid-gas mixture

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Phases

Solid liquid gas

ice water steam

One species of molecules can aggregate into several forms, known as phases.

actions and words

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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.

A bit of high-school mathematicsFour ways to represent

a function of two variables, f(x,y)

• Contour plot (plane diagram)• Table• A surface in 3D• An equation

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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

compressedliquid

saturatedliquid

coexistentLiquid and vapor

saturated vapor

superheated vapor

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Represent states on TV• 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 dome of coexistent phases

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Two paths to change from one state to another state

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P = 100 kPaTsat = 100 degCVf = 10-3 m3/kgVg = 1.7 m3/kg

https://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter2a.html

Heat causes giant motion when liquid turns to gas

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Represent states on PV

14https://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter2a.html

Saturation Temperature and Saturation Pressure

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liquid

gas

Two paths to change from one state to another state

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a P

a

a

T

critical point

a P

a

a

T

critical point

A path of discontinuous change of state A path of continuous change of state

liquid

gasliquid

gas

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Pressure cooker

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Invented by Denis Papin, France, 1679

P ~ 2 atmT ~ 120 dedC

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.

Bottled gas by liquefaction

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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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A partial listing of Table A–6.

Tables of properties outside the dome Compressed liquid or superheated vapor

Specify a state by values of PT

• Table A–4: Saturation properties of water under temperature.

• Table A–5: Saturation properties of water under pressure.

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A partial list of Table A–4.

Tables of properties in the domecoexistent liquid and vapor

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Specify a state of coexistent phases

Specify a state by values of two variables: TV or PV, but not PT.

Two more ways to specify a state of coexistent phases: Tx or Px.

0 < x < 1: mixture of liquid and vaporx = 0: saturated liquid x = 1: saturated vapor

Rule of mixture

Equation of state: An equation that relates properties of a substance.

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A bit of high-school scienceIdeal-gas law

Is Water Vapor an Ideal Gas?

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Principle of corresponding states• 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.

• 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.

Summary—states, properties, and phases

• 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.

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liquid

gas

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Three phases

Triple point

sublimation/condensation

evaporation/condensation

melting/freezing

liquid

30https://en.wikipedia.org/wiki/Water_(data_page)

Liquid water is denser than ice

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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

32http://www.wardteam.com/Blog/Preventing-Frozen-Pipes

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https://commons.wikimedia.org/wiki/File:Phase_diagram_of_water.svg

https://commons.wikimedia.org/wiki/File:Phase_diagram_of_water.svg

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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

Borgnakke and Sonntag, Fundamentals of Thermodynamics

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Project a surface in 3D to planes

Borgnakke and Sonntag, Fundamentals of Thermodynamics

Aggression in dogs

39Zeeman, Catastrophe theory. Scientific of American, 65 (1976)

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Phase diagram on P-V plane

Questions that motivate later lectures

1. What is temperature?2. What is a thermodynamic state?3. Why does a system isolated for a long time reach equilibrium?4. What is equilibrium?5. 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., co-

existent 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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