Use of Steam Tables

• Saturated Vapor or Liquid– Liquid at Bubble-Point

– Vapor at Dew-Point

– Liquid and Vapor Co-existing

• Superheated Vapor or Sub-Cooled Liquid– Vapor Above Dew-Point Temperature or Below Dew-

Point Pressure

– Liquid Below Bubble-Point Temperature or Above Bubble-Point Pressure

Vaporize 1kg Water at 20 C and Bubble Point Pressure

ˆ ˆ

ˆ ˆ

U Q W Q P V

m U Q mP V

Q m U P V

3 5

2

ˆ ˆ

2403.0 83.91

57.8 0.0010021 0.0234 1 10

1,000

2454.3

Q m U P V

kJkgQ

kg

mkg bar N kJ

kg m bar N m

Q kJ

H U PV

H U P V

Definitions

• Degrees of Superheat– Difference between actual temperature and

saturation temperature at the same pressure

• Degrees of Sub-Cooling– Difference between actual temperature and the

saturation temperature at the same pressure.

Vapor

Liquid

Water Vapor Heating1 kg from 100 oC, 1 Bar to 200 oC, 1 Bar

ˆ ˆ

ˆ ˆ ˆ

U Q W Q P V

m U Q mP V

Q m U P V m H

Water Vapor Heating1 kg from 100 oC, 1 Bar to 200 oC, 1 Bar

ˆ ˆ ˆ

2875 26761199

Q m U P V m H

kJkgQ kJ

kg

Constant Volume Water Vapor Heating1 kg from 100 oC, 1 Bar to 200 oC, P=?

0

ˆ

V

U Q

m U Q

barbarT

TPP 73.1

15.373

15.4731

1

212

Ideal Gas Law Estimation

Interpolation for Pressure

0

1

2

3

4

5

6

0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3

Specific Volume

Pre

ssu

re

Interpolation for Internal Energy

2640

2645

2650

2655

2660

0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3

Specific Volume

Inte

rnal

En

erg

y

Linear Interpolation

1 1 2 2

2 1 2 1

2 1

2 1

1 1

1 1

1 1

2 11 1

2 1

y mx b

y mx b y mx b

y y m x x

y ym

x x

b y mx

y mx y mx

y y m x x

y yy y x x

x x

2 11 1

2 1

2 1

1 1

2 1

ˆ ˆˆ ˆ

5 11 1.69 2.17 2.1

0.425 2.17ˆ ˆ

ˆ ˆ ˆ ˆˆ ˆ

2643 2658ˆ 2658 1.69 2.17 26540.425 2.17

ˆ 1 2654 2507 147

Desired

Desired

P PP P V V

V V

P bar

U UU U V V

V V

kJU

kg

kJQ m U kg kJ

kg