CPE 221 S02Lect 4

1

Pressure-Temperature Diagram for a Pure Substance

Temperature

Pres

sure

Solid

Subcooledor compressedLiquid

SuperheatedVapor

SupercriticalFluid or Gas

Sublimation

VLE

Fusion

Within each phase, the properties of the substance are functions of temperature and pressure.

Critical Point

Triple Point

CPE 221 S02Lect 4

2

Pv ZRT=

EQUATIONS OF STATE

Lee-Kesler Compressibility Charts

Recall the compressibility factor correction to the Ideal Gas Law:

In the Lee-Kesler charts, Z is a function of reduced temperature and pressure.

cr T

TT = (absolute temperatures, consistent units)

cr P

PP = (absolute pressures, consistent units)

Example: Calculate for ammonia at 240 °F and 800 psia.

Tc = 729.9 ºR; Pc = 1646 psia ; M = 17.031 (Table C.1)

v

(240 459.67) R 0.96729.9 R

800 psia 0.491646 psia

rc

rc

TTTPPP

+ °= = =°

= = =

CPE 221 S02Lect 4

3

Lee-Kesler Z chart, Sonntag, Borgnakke, Van Wylen, 1998.

CPE 221 S02Lect 4

4

3 310.7317 psi ft 699.67 R ft0.73 6.9lbmol R 800 psi lbmole

ZRTvP

⋅ °= = × × =⋅ °

Calculate :v

Calculate v:3 3

m m

6.9 ft lbmole ft0.40lbmole 17.031lb lb

v = × =

Note that the ideal gas law specific volume would be:

3 310.7317 psi ft 699.67 R ft9.4lbmol R 800 psi lbmole

RTvP

⋅ °= = × =⋅ °

3 3

m m

9.4 ft lbmole ft0.55lbmole 17.031lb lb

v = × =

What is the true specific volume?

CPE 221 S02Lect 4

5

TABLES AND CHARTS

Temperature

Pres

sure

Solid

Subcooledor compressedLiquid

SuperheatedVapor

SupercriticalFluid or Gas

Sublimation

VLE

Fusion

Critical Point

Triple Point

Steam Tables:

SI EnglishSaturated Liquid and Vapor B.1.1 (T entry)

B.1.2 (P entry) C.8.1Superheated Steam B.1.3 C.8.2Compressed Liquid B.1.4 C.8.3Saturated Solid and Vapor B.1.5 C.8.4

CPE 221 S02Lect 4

6

Pres

sure

Volume

Satu

rate

d Li

quid Saturated Vapor

v = x(vg) + (1-x)vf

x = % vapor= quality

Steam Tables, Sonntag, Borgnakke, Van Wylen, 1998.

CPE 221 S02Lect 4

7

Pres

sure

Volume

Satu

rate

d Li

quid Saturated Vapor

Steam Tables, Sonntag, Borgnakke, Van Wylen, 1998.

CPE 221 S02Lect 4

8

Steam Tables, Sonntag, Borgnakke, Van Wylen, 1998.

Pres

sure

Volume

Satu

rate

d Li

quid Saturated Vapor

CPE 221 S02Lect 4

9

Steam Tables, Sonntag, Borgnakke, Van Wylen, 1998.

Temperature

Pres

sure

Sublimation

VLE

Fusion

Critical Point

Triple Point

SL

V

CPE 221 S02Lect 4

10

Example: Calculate for ammonia at 300 °F and 2000 psia.

Tc = 729.9 ºR; Pc = 1646 psia ; M = 17.031 (Table C.1)

3

m

ft0.40lb

v =

3

m

ft0.55lb

v =

v

Ideal Gas:

Lee-Kesler Z:

Table C.9.2

AmmoniaTables, Sonntag, Borgnakke, Van Wylen, 1998.

CPE 221 S02Lect 4

11

THERMODYNAMIC SURFACES

Recall the general phase diagram for a pure component:

Temperature

Pres

sure

Sublimation

VLE

Fusion

Critical Point

Triple Point

SL

V

We can take a “slice” out of the VLE line and plot a property:

Pres

sure

Enthalpy

Satu

rate

d Li

quid Saturated Vapor

Temperature – Entropy diagrams are also common.

Pres

sure

Volume

Satu

rate

d Li

quid Saturated Vapor

T1

T2

T3

CPE 221 S02Lect 4

12

Pressure – Volume – Temperature Diagram:

Figure 3.11, Sonntag, Borgnakke, Van Wylen, 1998.