Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 1Additional Aspects for the P-V-T Surface for Water

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 2Additional Aspects for the P-V-T Surface for Water

Using Thermodynamic Using Thermodynamic TablesTables

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 3Additional Aspects for the P-V-T Surface for Water

Saturated Liquid and Saturated Liquid and Saturated vapor Saturated vapor StatesStatesA4 & A5A4 & A5

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 4Additional Aspects for the P-V-T Surface for Water

The two-phase region for waterThe two-phase region for water

pp

Saturated LiquidSaturated Liquid V

Saturated VaporSaturated Vapor

Critical PointCritical Point

gf VVV

fgfg vvv

FIGURE 2-30A partial list of Table A–4.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2-10

Enthalpy

• What does hfg represent?– Total amount of energy to change a saturated

liquid to a saturated vapor– Enthalpy of vaporization or latent heat of

vaporization.

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 7Additional Aspects for the P-V-T Surface for Water

Saturated Liquid-Vapor Saturated Liquid-Vapor MixturesMixtures

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 8Additional Aspects for the P-V-T Surface for Water

Quality...Quality...

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 9Additional Aspects for the P-V-T Surface for Water

Liquid-vapor equilibrium Liquid-vapor equilibrium

Liquid at P,TLiquid at P,T Surroundings

Vapor at P,TVapor at P,TVapor at P,T

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 10Additional Aspects for the P-V-T Surface for Water

QualityQuality

vaporliquid

vapor

mm

mx

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 11Additional Aspects for the P-V-T Surface for Water

Quality definedQuality defined

Quality, x, allows location of states inside Quality, x, allows location of states inside the vapor-liquid region.the vapor-liquid region.

gf vvv

pp

Vgvfv v

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 12Additional Aspects for the P-V-T Surface for Water

QualityQuality

vaporliquid

vapor

mm

mx

fg

fgf

vxxvv

xvvv

1

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 13Additional Aspects for the P-V-T Surface for Water

Internal energy in the vapor-liquid Internal energy in the vapor-liquid regionregion

fg

fgf

uxxuu

xuuu

)1(

The same holds for specific enthalpy, h

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 14Additional Aspects for the P-V-T Surface for Water

Superheated VaporSuperheated Vapor

Characterized by… p83Characterized by… p83

Table A6Table A6

FIGURE 2-40A partial listing of Table A–6.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2-11

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 16Additional Aspects for the P-V-T Surface for Water

Compressed LiquidCompressed LiquidCharacterized by… p84 Characterized by… p84 Tables A7 or A4 & A5Tables A7 or A4 & A5Can treat as saturated Can treat as saturated liquid at Temperature.liquid at Temperature.Exception is enthalpyException is enthalpy

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 17Additional Aspects for the P-V-T Surface for Water

Reference States and ValuesReference States and Values

• For energies, entropies, and enthalpies, can only calculate changes and can’t measure.

• Must pick a zero point.– for water, saturated liquid at 0.01°C

– for refrigerant-134a, saturated liquid at -40°C

• OK as long as you are consistent.

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 18Additional Aspects for the P-V-T Surface for Water

EQUATIONS OF EQUATIONS OF STATE FOR GASES:STATE FOR GASES:

Equation that relates the pressure, temperature, and specificVolume of a substance.

Gas vs. vapor?

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 19Additional Aspects for the P-V-T Surface for Water

Definition of gas...Definition of gas...

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 20Additional Aspects for the P-V-T Surface for Water

Fluids and gassesFluids and gasses

A liquid will take the shape of its containerbut exhibits a free surface.

A liquid will take the shape of its containerbut exhibits a free surface.

A gas will fill its containercompletely and does notexhibit a free surface.

A gas will fill its containercompletely and does notexhibit a free surface.

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 21Additional Aspects for the P-V-T Surface for Water

The ideal gas...The ideal gas...

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 22Additional Aspects for the P-V-T Surface for Water

P-V-T relation for ideal gasesP-V-T relation for ideal gasesTT11

TT22

TT33

pp

T

vp

RT

vp

p

lim0

Bar means on a molarbasis

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 23Additional Aspects for the P-V-T Surface for Water

The ideal gas equation of stateThe ideal gas equation of state

TRvp This implies: (1) very little molecular interaction (p 0),and (2) molecules are point masses, i.e., zero volume.

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 24Additional Aspects for the P-V-T Surface for Water

The universal gas constantThe universal gas constant

Rlbmollbfft

KkmolkJ

RMR

/1545

/314.8

M = Molecular weight, kg/kmol M = Molecular weight, kg/kmol or lbm/lbmol.or lbm/lbmol.

Universal – p88 (2-11)Specific – Table A-1 p824

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 25Additional Aspects for the P-V-T Surface for Water

The ideal gas state surfaceThe ideal gas state surfaceIdeal Gas State Surfacepp

VTT

Instructor’s Visual AidsHeat Work and Energy. A First Course in Thermodynamics© 2002, F. A. Kulacki

Chapter 2 Module 2 Slide 26Additional Aspects for the P-V-T Surface for Water

Water?Water?

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

FIGURE 2-49Percentage of errorinvolved in assuming steam to be an ideal gas, and the region where steam can betreated as an ideal gas with less than 1 percent error.

2-12