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

• A substance: a collection of molecules or atoms• A pure substance: A substance that has a homogeneous composition.

• 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.

2

Pure Substance

Liquid-gas mixture

3

4

Phase

Solid liquid gas

ice water steam

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

System

5

Experimental setup: cylinder-piston device•A fixed number of H2O molecules•Cylinder, rigid.•Piston, frictionless.•Weights•Fire

liquid

weights

fire

vapor

• A system can be any part of the world.• The rest of the world is called the surroundings of the system.

Isolated system

6

• 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.

liquid

weights

fire

vapor liquid

vapor

isolated system

State

7

• 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.

liquid

weights

fire

vapor liquid

vapor

isolated system

Property

8

• 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)

liquid

weights

fire

vapor liquid

vapor

isolated system

Intensive and extensive properties

• 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.

9

Specific volume

10

High-school mathematicsFour ways to represent a function of two independent variables, z(x,y)

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

11

12

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

compressedliquid

saturatedliquid

coexistentLiquid and vapor

saturated vapor

superheated vapor

13

Represent states on the T-v plane• 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)

liquid

weights

fire

vapor

14

The discovery of the domeA 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)

15

Two paths to change from one state to another state

A path of continuous change of state

A path of discontinuous change of state

16

A state of coexistent phasesSpecify a state of coexistent phases by values of two variables (T,v) or (P,v), but not (P,T).

Two more ways to specify a state of coexistent phases: (T,x) or (P,x).

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

Specific volume follows rule of mixture

vf vgv

T

v

vf specific volume of saturated liquidvg specific volume of saturated gasv specific volume of a mixture of liquid and gas

Define quality by

Volume is additive

Volume and specific volume

17

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 changes to gas

18

Represent states on PV

19https://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter2a.html

Saturation Temperature and Saturation Pressure

20

liquid

gas

Two paths to change from one state to another state

21

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

22

Pressure cooker

23

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

24

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

25

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.

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

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

26

A partial list of Table A–4.

Tables of properties inside the domecoexistent liquid and vapor

27

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

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

28

A bit of high-school scienceIdeal-gas law

Is Water Vapor an Ideal Gas?

29

30

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.

31

van der Waals Equation of State

Critical isotherm of a pure substance has an inflection point at the critical point.

a P

a

a T

critical point

Summary—system, state, property, and phase

• 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.

32

liquid

gas

33

Three phases

Triple point

sublimation/condensation

evaporation/condensation

melting/freezing

liquid

34https://en.wikipedia.org/wiki/Water_(data_page)

Liquid water is denser than ice

35

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

36http://www.wardteam.com/Blog/Preventing-Frozen-Pipes

37https://commons.wikimedia.org/wiki/File:Phase_diagram_of_water.svg

38

Phase diagram unlike that of water

39

40

The function P(T,V)

41

Project a surface in 3D to planes

Borgnakke and Sonntag, Fundamentals of Thermodynamics

42

Project a surface in 3D to planes

Borgnakke and Sonntag, Fundamentals of Thermodynamics

43

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 the molecular picture of 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?

44