# Steam and Vapor Enthalpy

## Introduction and definition of vapor and steam enthalpy - specific enthalpy of saturated liquid, saturated vapor and superheated vapor

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When a liquid evaporates its go through a process where

- the liquid heats up to the evaporation temperature
- the liquid evaporate at the evaporation temperature by changing state from fluid to gas
- the vapor heats above the evaporation temperature - superheating

The heat transferred to a substance when temperature changes is often referred to as **sensible heat**. The heat required for
changing state as evaporation is referred to as **latent heat of evaporation**.

The most common vapor is evaporated water - steam or moist.

### Enthalpy

Enthalpy of a system is defined as the mass of the system - *m* - multiplied by the specific enthalpy - *h* - of the system and
can be expressed as:

H = m h(1)

where

H= enthalpy (kJ)

m= mass (kg)

h= specific enthalpy (kJ/kg)

### Specific Enthalpy

Specific enthalpy is a property of the fluid and can be expressed as:

h = u + p v(2)

where

u= internal energy (kJ/kg)

p= absolute pressure (N/m^{2})

v= specific volume (m^{3}/kg)

Part of the water vapor - steam - properties can be expressed in a table as:

p (bar) |
t_{s
} (^{o}C) |
v_{f
} (m^{3}/kg) |
v _{g
}(m^{3}/kg) |
u_{f
} (kJ/kg) |
u_{g
} (kJ/kg) |
h_{f
} (kJ/kg) |
h _{g
}(kJ/kg) |
s_{f
} (kJ/kg.K) |
s_{g
} (kJ/kg.K) |
---|---|---|---|---|---|---|---|---|---|

0.006112 ^{1)} |
0.01 | 0.0010002 | 206.1 | 0 | 2,375 | 0.0006 | 2,501 | 0 | 9.155 |

0,010 | 7.0 | 0.0010001 | 129.2 | 29 | 2,385 | 29 | 2,514 | 0.106 | 8.974 |

. | . | . | . | . | . | . | . | . | . |

1.01325 ^{2)} |
100.0 | 0.001044 | 1.673 | 419 | 2,507 | 419 | 2,676 | 1.307 | 7.355 |

. | . | . | . | . | . | . | . | . | . |

220 | 373.7 | 0.00269 | 0.00368 | 1,949 | 2,097 | 2,008 | 2,178 | 4.289 | 4.552 |

221.2 ^{3)} |
374.15 | 0.00317 | 0.00317 | 2,014 | 2,014 | 2,084 | 2,084 | 4.430 | 4.430 |

*s*is the steam entropy- suffix -
*f -*referrer to saturated liquid - suffix -
*g -*referrer to saturated vapor - steam

Internal energy - *u* - can be calculated from (2) and is often omitted in tables. *v** _{f}* - change very little
and is also often omitted.

^{1)}referrer to absolute vacuum.^{2)}referrer to water boiling at standard atmosphere.^{3}^{)}referrer to water critical point. For pressures above the critical point there is no definite transition from liquid to vapor.

### Specific Enthalpy of Saturated Water

Specific enthalpy of saturated water - *h*_{f} - can be obtained from tables as above. The value depends on the
pressure.

For saturated water at standard atmosphere - ^{2)} -the specific enthalpy - *h*_{f} - is
*419 kJ/kg*. At
standard atmosphere - *1 bar (14.7 psi) *- water starts boiling at *100 ^{o}C (212 ^{o}F).*

The specific enthalpy of water (in SI units) can be calculated from:

h_{f}= c_{w}(t_{f}- t_{0})(3)

where

h_{f}= enthalpy of water (kJ/kg)

c_{w}= specific heat of water = 4.19 (kJ/kg.^{o}C)

t_{f}= saturation temperature (^{o}C)

t_{0}= refer temperature = 0 (^{o}C)

### Specific Enthalpy of Saturated Steam

Specific enthalpy of saturated steam - *h _{g}* - can be obtained from tables as above. The value depends on the pressure.

For saturated steam at standard atmosphere - ^{2)} - the specific enthalpy - *h _{g}* - is

*2676 kJ/kg*.

The specific enthalpy of evaporation can be calculated from:

h_{e}= h_{g}- h_{f}(4)

where

h_{e}= specific evaporation enthalpy (kJ/kg)

Specific evaporation enthalpy for water at standard atmosphere is:

h_{e}=(2676 kJ/kg) - (419 kJ/kg)

= 2257 (kJ/kg)

### Specific Enthalpy of Superheated Steam

The specific enthalpy of superheated steam can be calculated from:

h_{s}= h_{g}+ c_{ps}(t_{s}- t_{f})(5)

where

h_{s}= enthalpy of superheated steam (kJ/kg)

c_{ps}= specific heat of steam at constant pressure = 1.860 (kJ/kg^{o}C)

t_{f}= saturation temperature (^{o}C)

t_{s}= superheated steam temperature (^{o}C)

*c _{ps}*

*= 1.860 (kJ/kg*at standard atmosphere. Be aware that

^{o}C)*c*varies with temperature.

_{ps}### Common Units for Specific Enthalpy

*1 kJ/kg = 1,000 J/kg**1 erg/g = 1E-4 J/kg**1 Btu/lbm = 2,326 J/kg**1 cal/g = 4,184 J/kg*

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