ME152 1

Properties of Pure Substances

Reading: Cengel & Boles, Chapter 2

ME152 2

Liquid & Vapor Phases of a Pure Substance

• Compressed (subcooled) liquid• Saturated liquid • Saturated liquid-vapor mixture

• Saturated vapor • Superheated vapor

ME152 3

Saturation Pressure & Temperature• “Saturation” refers to phase change,

typically liquid-vapor

• The saturation temperature, Tsat , is the boiling point at a specified pressure

• The saturation pressure, Psat , is the pressure at the boiling point

• Saturation temperature and pressure are dependent properties

• The latent heat of vaporization is the energy absorbed during vaporization or released during condensation

ME152 4

Thermodynamic Properties

• Pressure, P• Temperature, T• Volume, V

– specific volume, v = V/m• Internal energy, U

– specific internal energy, u = U/m• Enthalpy, H

– specific enthalpy, h = H/m• Entropy, S

– specific entropy, s = S/m• Quality, x

ME152 5

New Properties

• Enthalpy - property of “convenience”, primarily used in control volume analysis

• Quality - intensive property used to describe saturated, liquid-vapor states

enthalpy) (specific

enthalpy) (total

PvumHh

PVUH

vaporliquid

vapor

mmm

x

mixture saturated of mass total vaporsaturated of mass

ME152 6

New Properties, cont.

• Quality is used to describe saturated states only– Saturated liquid: x = 0– Saturated liquid-vapor mixture: 0< x <1– Saturated vapor: x = 1

• Quality-property relationships (where y = v, u, h, or s):

fgf

fgf

fg

f

fg

f

xyy

yyxyy

yyy

yyyy

x

)(

ME152 7

Thermodynamic Property Data

• Based upon expt’l measurements• Compiled in tables, graphs, and

computer software• Text tables (Cengel & Boles)

– SI units: A-1 to A-29– (English units: A-1E to A-29E)

– H2O properties: A-4 to A-8– R-134a properties: A-11 to A-13– Selected solid & liquid properties: A-3– Ideal gas properties: A-2, A-17 to A-25– Thermochemical properties: A-26 to A-28

ME152 8

Property Tables (Cengel & Boles)• Table A-1: molecular weight (M),

critical properties (Tcr, Pcr)• Phase tables:

ME152 9

Compressed Liquid Properties

• Compressed liquid property tables are usually not available because these properties are relatively independent of pressure

• General approximation for v, u, h, and s as a compressed liquid:

• The approximation for h at higher pressures can be improved using

TfTfTfTf sshhuuvv @@@@ , , ,

)( @@@ TsatTfTf PPvhh

ME152 10

The State Postulate

• General rule for determining the number of independent, intensive properties needed to specify a state of a system:

N = 1 + [no. of work interactions]

• Simple, Compressible System – refers to system with only one type of work interaction – compression-expansion work – therefore, only two independent, intensive properties are needed to specify a state

ME152 11

The Ideal Gas Equation of State

• Equation of state - any equation that relates P, v, and T

• Gas - a superheated vapor, usually where T > Tcr

• Experiments with gases show that

• This constant is known as the universal gas constant, Ru , which has a value of 8.314 kJ/kmol-K

constant lim0

TPvM

P

ME152 12

The Ideal Gas Equation of State, cont.• The resulting equation is often called

the ideal gas law, written as

where R is the gas constant and M is the molecular weight (mass):

• Other forms:

RTPv K] - [kJ/kg /M R Ru

TRvPTNRPV

mRTPV

u

u

ME152 13

The Ideal Gas Equation of State, cont.

• For closed system analysis (m = constant), the PV=mRT form is very useful:

– where 1 and 2 refer to the gas properties at two different states

2

22

1

11

TVP

TVP

ME152 14

When is the Ideal Gas Equation of State Valid?

• Can be used for light gases such as air, N2, O2, H2, He, Ar, Ne, Kr, and CO2 at relatively low pressure or high temperature:

• The ideal gas law is generally not valid for water vapor in steam power plants or refrigerant vapors in refrigeration or heat pump systems (use property tables for these!)

2/or 05.0/ crcr TTPP

ME152 15

The Compressibility Factor

• The deviation from ideal gas behavior is quantified by the compressibility factor, Z :

• Z = 1 is an ideal gas; real gases may have Z < 1 or Z > 1

• The generalized compressibility chart (see Figures A-30a,b,c) allows evaluation of Z using a reduced pressure and reduced temperature:

RTPvZ

crRcrR TTTPPP / , /

ME152 16

Specific Heat

• Specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree

• The required energy depends upon how the process is executed:– constant volume

– constant pressure

K]-[kJ/kg v

v TuC

K]-[kJ/kg P

p ThC

ME152 17

Specific Heat, cont.

• Specific heats (Cv, Cp) are properties and do not depend upon the process

• Cp Cv because additional energy must be supplied for the work performed that allows the system to expand at constant pressure

• Specific heat for a particular substance can change with temperature and pressure

ME152 18

Specific Heats of Ideal Gases• Experiments show that u = u(T) and

h = h(T) for ideal gases; therefore:

• Separating variables and integrating yields

• We need Cv(T) and Cp(T) to carry out these integrations

dTdhC

dTduC pv and

2

112

2

112

dTChh

dTCuu

p

v

ME152 19

Specific Heats of Ideal Gases, cont.• There are three approaches to

evaluating u2-u1 and h2-h1 :

– using tabulated u and h data (Tables A-17 to A-25); easiest and most accurate

– using polynomial relations for Cv and Cp as a function of T (Table A-2c) and integrating; accurate but tedious

– using a constant specific heat at the average temperature (Table A-2b); simple and reasonably accurate; very convenient when u, h tables are not available

ME152 20

Constant Specific Heat Approach• Integrations yield:

– where the average specific heats are evaluated from Table A-2b at the average temperature (T1+T2)/2

• This approach is exact for monatomic gases such as He, Ne, and Ar because their specific heats are independent of temperature

)(

)(

12,12

12,12

TTChh

TTCuu

avp

avv

ME152 21

Specific Heat Relations

• For ideal gases,

• Differentiating wrt T,

• Define specific heat ratio, k :

RTuPvuh

RCCRdTdu

dTdh

vp or

vv

p

CR

CC

k 1

ME152 22

Specific Heats of Incom-pressible Substances

• Solids and liquids are considered incompressible substances

• Since volume remains constant for incompressible substances,

• Since u = u(T) for incompressible substances, we have

– where Cav is found in Table A-3 for solids and liquids at the average temperature (T1+T2)/2

CCC vp

)( 12

2

112 TTCCdTuu av

ME152 23

Specific Heats of Incom-pressible Substances, cont.

• Enthalpy change,

• For constant pressure processes,

• For constant temperature processes,

)()( 121212 PPvTTChhvdPdudh

av

)( 1212 TTChh av

)( 1212 PPvhh