Properties of Pure Substances

Chapter 3

Why do we need physical properties?

As we analyze thermodynamic systems we describe them using physical properties

Those properties become the input to the equations we’ll use to solve thermodynamic problems

Pure Substance

In Chemistry you defined a pure substance as an element or a compound

Something that can not be separatedIn Thermodynamics we’ll define it as

something that has a fixed chemical composition throughout

Examples

Ice in equilibrium with pure water

AirAir in equilibrium

with liquid air is not a pure substance – Why?

Phases of Pure Substances

We all have a pretty good idea of what the three phases of matter are, but a quick review will help us understand the phase change process

Solid

Long range order Three dimensional

pattern Large attractive

forces between atoms or molecules

The atoms or molecules are in constant motion – they vibrate in place

The higher the temperature – the more vibration This image is the property of IBM

http://www.kings.edu/~chemlab/vrml/

Platinum Atoms

Liquid

When a solid reaches a high enough temperature the vibrations are strong enough that chunks of the solid break of and move past each other

Short range order Inside the chunks the

atoms or molecules look a lot like a solid

Ex. You only break 5% to 15% of the water hydrogen bonds to go from solid to liquid

http://www.earth-photography.com/Countries/Norway/Norway_Jostedalsbreen_Glacier4.html

Gas

Molecules are far apartNo long or short range

orderHigh kinetic energyIn order to liquefy, lots

of that kinetic energy must be released

http://pisces.sdsu.edu/ONLINE_LESSONS/WEATHER/

Solid to Liquid to Gas

On a molecular level, the difference between the phases is really a matter of degree

We identify melting points and vaporization points based on changes in propertiesEx – big change in specific volume

Consider what happens when we heat water at constant pressure

Piston cylinder device – maintains constant pressure

T

v

1

2

5

3 4 Liquid to Gas Phase Change

Liquid to Gas Phase Change

Liquid to Gas Phase Change

Two Phase Region

Compressed Liquid

Superheated Gas

Critical Point

Critical Point

Above the critical point there is no sharp difference between liquid and gas!!

Pressure-volume diagram

Property Diagrams

So far we have sketchedT – v diagramP – v diagramWhat about the P – T diagram?

Property Diagrams

Combine all three

You can put all three propertiesPTV

On the same diagram

3 Dimensional Phase DiagramsExpands on Freezing Contracts on Freezing

State Postulate

The state of a simple compressible system is completely specified by two independent, intensive properties

State Postulate

Remember that during a phase change, Temperature and Pressure are not independent

Property Tables

P - pressureT - temperaturev – specific volumeu – specific internal energyh – specific enthalpy h = u + Pvs – specific entropy -define in Chapter 7

A word about enthalpy

Enthalpy is a combination propertyh=u+PvH=U+PV

It is useful because it makes some equations easier to solve

You could do all of thermodynamics without it – but its more convenient to use it.

Saturated Liquid and Saturated Vapor States

Saturation Properties

Saturation Pressure is the pressure at which the liquid and vapor phases are in equilibrium at a given temperature.

 Saturation Temperature is the

temperature at which the liquid and vapor phases are in equilibrium at a given pressure.

Table A-4 and A-5

A-4 pg 890Saturated water temperature table

A-5 pg 892Saturated water pressure table

u u u

h h h

s s s

fg g f

fg g f

fg g f

g stands for gas

f stands for fluid

fg stands for the difference between gas and fluid

Transitions from liquid to gas

Quality

xmass

mass

m

m msaturated vapor

total

g

f g

Fraction of the material that is gasx = 0 the material is all saturated liquid

x = 1 the material is all saturated gas

x is not meaningful when you are out of the saturation region

Quality

X = 0 X = 1

Average Properties

y y x y y

y x yf g f

f fg

( )

When x = 0 we have all liquid, and y = yf

0

When x = 1 we have all gas, and y = yf + yfg = yg

1= yg

Superheated Properties

Table A-6, pg 894

Compressed Liquid

y y f T @

h h v P Pf T f sat @ ( )

We only need to adjust h if there is a big difference in pressure

Linear Interpolation

A B

100 5

200 10

130 X 510

5

100200

100130

x

Equations of State

Equations vs Tables

The behavior of many gases (like steam) is not easy to predict with an equation

That’s why we have tables like A-4, A-5 and A-6

Other gases (like air) follow the ideal gas law – we can calculate their properties

Ideal Gas Law

PV=nRTUsed in your Chemistry classFrom now on we will refer to the gas

constant , R, as the universal gas constant, Ru , and redefine R=Ru/MW

PV=mRTR is different for every gasTabulated in the back of the book

PV=nRuT

Ideal Gas Law

v = V/mPv = RT

This is the form we will use the most

Relates 3 properties

P, v and T

When does the ideal gas law apply?

The ideal gas equation of state can be derived from basic principles if one assumes: 1. Intermolecular forces are small

2. Volume occupied by the particles is small

These assumptions are true when the molecules are far apart – ie when the gas is not dense

Criteria

The ideal gas law applies when the pressure is low, and the temperature is high - compared to the critical values

The critical values are tabulated in the Appendix

Is Steam an Ideal Gas?

Compressibility Factor

You can adjust the ideal gas law with a fudge factor, called the compressibility factor

Pv = z RTz is just a value you put in to make it

work outz = 1 for ideal gases

Principle of Corresponding States

The Z factor is approximately the same for all gases at the same reduced temperature and reduced pressure

TT

TP

P

PRcr

Rcr

and

Comparison of z factors

What do you do when P or T is unknown?

vvRTP

Ractual

cr

cr

Check out Appendix A-15 pg 908

Other Equations of StateVan der Waals

( )( )Pa

vv b RT

2

aR T

Pb

RT

Pcr

cr

cr

cr

27

64 8

2 2

and

Beattie-Bridgeman

PR T

v

c

vTv B

a

vu FHG

IKJ

2 3 21 ( )

A Aa

vB B

b

vo o FHG

IKJ F

HGIKJ1 1 and

Benedict-Webb-Rubin

PR T

vB R T A

C

T v

bR T a

v

a

v

c

v T ve

uo u o

o u

v

FHG

IKJ

FHG

IKJ

2 2 3

6 3 2 2

1

12 /

Percentage Error for Nitrogen

Summary

In this Chapter we learnedHow the state of a substance changes

with Temperature and PressureHow to read and use property tablesWhen we can use the ideal gas lawAlternative equations of state