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 atoms A pure substance: A substance that has the same composition everywhere. 3 Pure Substance

Liquid-gas mixture 4

5 Phases Solid liquid gas ice water steam One species of molecules can aggregate into several forms, known as phases.

actions and words 6 Parts of an experimental setup A fixed number of H 2 O molecules Cylinder Frictionless, perfectly sealed piston Weights Fire System A fixed number of H 2 O 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 mathematics Four ways to represent a function of two variables, f(x,y) Contour plot (plane diagram) Table A surface in 3D An equation 7

8 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 compressed liquid saturated liquid coexistent Liquid and vapor saturated vapor superheated vapor

9 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

10 The dome of coexistent phases

11 Two paths to change from one state to another state

12 P = 100 kPa T sat = 100 degC V f = m 3 /kg V g = 1.7 m 3 /kg Heat causes giant motion when liquid turns to gas

13 Represent states on PV

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Saturation Temperature and Saturation Pressure 15 liquid gas

Two paths to change from one state to another state 16 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 gas liquid gas

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Pressure cooker 18 Invented by Denis Papin, France, 1679 P ~ 2 atm T ~ 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 19 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, NH 3 liquid gas

20 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.

21 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. 22 A partial list of Table A–4. Tables of properties in the dome coexistent liquid and vapor

23 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 vapor x = 0: saturated liquid x = 1: saturated vapor Rule of mixture

Equation of state: An equation that relates properties of a substance. 24 A bit of high-school science Ideal-gas law

Is Water Vapor an Ideal Gas? 25

26 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/P cr, T/T cr ) is nearly the same for all substances.

27 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: H 2 O. 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. 28 liquid gas

29 Three phases Triple point sublimation/cond ensation evaporation/cond ensation melting/freezing liquid

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Liquid water is denser than ice 31 The crystalline structure of ice is very open. Liquid water packs tighter. Ice floats on top of water

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33 ase_diagram_of_water.svg

34 Phase diagram unlike that of water

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36 The function P(T,V)

37 Project a surface in 3D to planes Borgnakke and Sonntag, Fundamentals of Thermodynamics

38 Project a surface in 3D to planes Borgnakke and Sonntag, Fundamentals of Thermodynamics

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

40 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? 41