1

Lec 5: Thermodynamic properties, Pvt behavior

2

• For next time:– Read: § 3-5– HW 3 due Sept 17

• Outline:– Buoyancy and stability– Pure substances and processes– Property diagrams for pure substances

• Important points:– How to calculate point of action of hydrostatic load– The general shape of the property diagrams– How to solve problems using the property diagrams

3

Properties - Introduction

• We have discussed extensive properties such as U, m, and V (for volume) which depend on the size or extent of a system, and

• Intensive properties such as u, v, T, and P which are independent of system extent (engineers are ambivalent about nomenclature for pressure, sometimes using p and P interchangeably)

4

Important questions...

• How many properties are needed to define the state of a system?

• How do we obtain those properties?

5

For a simple system,

• We may write: p = p(v,T)

• or perhaps: v = v(p,T).

6

Pure

• Pure means “…of uniform and invariable chemical composition (but more than one molecular type is allowed).” This allows a single phase of air to be a pure substance.

• All our substances will be pure. We will drop the use of the word. When we refer to a simple system we mean one filled with a pure substance--a simple, pure system.

7

For a simple, pure substance

• y1 = f(y2,y3), or

• p = p(v,T), v = v(p,T) and T = T(p,v)

• What do these equations define, in space?

• Equations used to relate properties are called “equations of state”

8

Ideal gas “law” is a simple equation of state

RTPvM

RR u

Ru = universal gas constant

m = mass

n = number of moles

M = molar mass or molecular weight

mRTPV TnRPV u

9

Behavior of real substances

• Lets consider substances that do not obey the perfect gas law– certainly not as a solid– certainly not as a liquid– sometimes not very well as a gas

10

Phase Change Process of a Pure Substance

P=1 atmT=20°C

P=1 atmT=100°C

P=1 atmT=100°C

P=1 atmT=250°C

P=1 atmT=100°C

liquid liquid liq/vap

vapor vapor

11

Consider a constant pressure process (of water)

12

T-v Diagram

13

14

You should be able to discuss characteristics of the following:

• Liquid to liquid/vapor to vapor transition (begin with a constant pressure process).

• Single phase regions--liquid, vapor, solid.• Two-phase regions--liquid/vapor and

solid/vapor.• Melting--solid to liquid (freezing)• vaporization--liquid to vapor (liquefaction)• sublimation--solid to vapor

15

16

Notice the triple-state line. Along this line all

three states exist in equilibrium

For water, the triple point is at 273.16 K (32.018 F) and 0.6113 kPa (0.0887 psia).

17

Vapor Dome - region encompassing the two-phase, vapor-liquid equilibrium region

Saturated vapor line

Saturated liquid line

18

Critical Point

• Point at which the saturated vapor and saturated liquid lines coincide.

• If T Tc or P Pc there is no clear distinction between the superheated vapor region and the compressed liquid region.

• Substances in this region are sometimes known as “fluids” rather than as vapors or liquids.

• By convention, if P Pc, and T Tc we refer to the fluid as superheated. If P Pc, and T < Tc we refer to the fluid as a subcooled or compressed liquid.

19

Phase Diagram (PT-coordinates)

P

T

Solid PhaseRegion

LiquidPhaseRegion

Superheated G asPhase Region

M eltingCurve

T rip leState

CriticalState

20

GAS @ gGAS

State d

W eight

LIQUID

GAS

W eight

LIQUID @ a

P

T

g

P

T

g

d

P

T

g

d

a

Superheated Vapor

Compressed Liquid

Constant Temperature Process

Q

21

P

T

b

Gas @ bGas @ b

Q

GAS

STATE f

LIQUID

Q

GASLIQUID

Q

P

T

bf

P

T

bfa

Superheated Vapor

Subcooled Liquid

Constant Pressure Process

22

23

P

v

Superheated Region

Saturation Region

Subcooled Region

Critical Point

Sat. Vapor Line

Sat. Liquid Line

24

25

Saturation temperature

• Temperature at which a phase change takes place at a given pressure.

26

Saturation pressure

• Pressure at which a phase change takes place at a given temperature.

27

TEAMPLAYTEAMPLAY

• Discuss what happens when water boils on the stove at your residence. Start with a pan of water at 70 F, 1 atm pressure.

QContinued on next slide.

28

TEAMPLAY (CONTINUED)TEAMPLAY (CONTINUED)• What is the pressure at various times

during the entire process?

• Does the temperature of the water change?

• If the vapor (steam) were contained in an elastic container, what would happen as heat continued to be added after all the liquid disappeared.

• Sketch pV and TV diagrams.

29

Saturation properties

• Along the saturated liquid line, properties are identified by the subscript “f”

• Along the saturated vapor line, properties are identified by the subscript “g”

•Both sets of properties can be found in the temperature and pressure tables in your book’s appendices.

•Both tables give the same data.

•There are different tables for different substances.

30

Temperature table (also known as a saturation table)

Table A-4

31

Pressure table (also known as a saturation table)

Table A-5

32

[Two properties are not independent in the vapor dome

(the two-phase region)]

• The temperature and pressure are uniquely related. Knowing a T defines the P and vice versa.

33

TEAMPLAYTEAMPLAY

• Find, for Refrigerant 134a, the following properties: the saturation pressure at a saturation temperature of -10 F.

• and find for the same substance the saturation temperature at a pressure of 0.06 MPa.

• Make sure everyone in your group understands how to do this.