Steam and Vapor Enthalpy

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/m²)

v = specific volume (m³/kg)

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

For full table with Enthalpy and Entropy - rotate the screen!

• 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 ^oC (212 ^oF).

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

h_f = c_w (t_f - t₀)                         (3)

where

h_f = enthalpy of water (kJ/kg)

c_w = specific heat water (4.19 kJ/kg. ^oC)

t_f = saturation temperature (^oC)

t₀ = refer temperature = 0 (^oC)

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 ^oC)

t_f = saturation temperature (^oC)

t_s = superheated steam temperature (^oC)

c_ps = 1.860 (kJ/kg ^oC) at standard atmosphere. Be aware that c_ps varies with temperature.

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