# Steam and Vapor Enthalpy

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

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 - super-heating

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 | 2375 | 0.0006 | 2501 | 0 | 9.155 |

0.010 | 7.0 | 0.0010001 | 129.2 | 29 | 2385 | 29 | 2514 | 0.106 | 8.974 |

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

1.01325 ^{2)} | 100.0 | 0.001044 | 1.673 | 419 | 2507 | 419 | 2676 | 1.307 | 7.355 |

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

220 | 373.7 | 0.00269 | 0.00368 | 1949 | 2097 | 2008 | 2178 | 4.289 | 4.552 |

221.2 ^{3)} | 374.15 | 0.00317 | 0.00317 | 2014 | 2014 | 2084 | 2084 | 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 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)

### Example - Energy to Evaporate Water

The energy to evaporate a certain amount of water can be calculated as

*Q = h _{e} m (4b)*

*where *

*Q = evaporation energy (kJ)*

*m = mass of water (kg)*

The energy to evaporate *5 kg* of water at atmospheric pressure can be calculated as

*Q = ( 2257 kJ/kg) (5 kg)*

* = 11285 kJ *

### 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 = 1000 J/kg**1 erg/g = 1E-4 J/kg**1 Btu/lbm = 2326 J/kg**1 cal/g = 4184 J/kg*

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