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# Steam Entropy

## Basic steam thermodynamics - entropy diagram.

The entropy diagram for steam shows the relationships between

• Pressure
• Temperature
• Dryness Fraction
• Entropy

With two factors given - the others can be found in the diagram. The ordinates in the diagram represents the Entropy and the Absolute temperature.

The diagram consist of the following lines

• Isothermal line
• Pressure lines
• Lines of dryness fraction
• Waterline between water and steam
• Dry steam lines
• Constant volume lines

The total heat is given by the area enclosed by absolute zero base water line and horizontal and vertical line from the respective points.

An adiabatic expansion is a vertical line. An adiabatic process is expansion at constant entropy with no transfer of heat.

• Critical temperature of steam is 375 to 3,380oC
• Critical pressure is 217.8 atm

### Total Entropy of Steam

#### Entropy of Water

The change of entropy can be expressed as:

dS = loge(T1/T)                               (1)

where

T = absolute temperature (K)

The entropy of water above freezing point can be expressed as:

dS = loge(T1/273)                            (2)

#### Entropy of Evaporation

Change of Entropy during evaporation

dS = dL/T                              (3)

where

L = latent heat (J)

#### Entropy of wet steam

The entropy of wet steam can be expresses as:

dS = loge(T1/273) + ζ(L1/T1)                              (4)

where

#### Entropy of superheated steam

Change of entropy during super-heating can be expressed as

dS = cp loge( T/T1 )                                (5)

where

cp= specific heat capacity at constant pressure for steam (kJ/kgK)

The entropy of superheated steam can be expressed as:

dS = loge( T1/273 ) + L1/T1 + cp loge( Ts/T1 )                                           (6)

where

Ts = absolute temperature of superheated steam

T1 = absolute temperature of evaporation

### Water and Steam Entropy - Imperial Units

Temperature
(oF)

Absolute Pressure
(psia)

Entropy (Btu/lb oF)
WaterSteam
0 0.0185 -0.3243 2.330
10 0.0309 -0.3141 2.283
20 0.0505 -0.3038 2.238
30 0.0809 -0.2936 2.195
32 (0 oC) 0.0887 0.0000 2.187
40 0.1217 0.0162 2.159
50 0.1718 0.0361 2.126
60 0.2564 0.0555 2.094
70 0.3633 0.0746 2.064
80 0.5074 0.0933 2.035
90 0.6989 0.1116 2.008
100 0.9503 0.1296 1.982
110 1.277 0.1473 1.957
120 1.695 0.1647 1.933
130 2.226 0.1817 1.911
140 2.893 0.1985 1.889
150 3.723 0.2151 1.868
160 4.747 0.2314 1.848
170 5.999 0.2474 1.829
180 7.519 0.2632 1.811
190 9.350 0.2787 1.793
200 11.54 0.2941 1.776
210 14.12 0.3092 1.760
212 (100 oC) 14.70 0.3122 1.756
220 17.20 0.3241 1.744
230 20.80 0.3389 1.729
240 24.99 0.3534 1.714
250 29.85 0.3678 1.700
• 1 psi (lb/in2) = 6894.8 Pa (N/m2)
• 1 Btu/(lbm oF) = 4186.8 J/ (kg K)

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Temperature

oC
oF

Length

m
km
in
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yards
miles
naut miles

Area

m2
km2
in2
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miles2
acres

Volume

m3
liters
in3
ft3
us gal

Weight

kgf
N
lbf

Velocity

m/s
km/h
ft/min
ft/s
mph
knots

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O

Flow

m3/s
m3/h
US gpm
cfm

3 30