Post on 31-Mar-2015
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