Enthalpy in Intensive Units – Specific Enthalpy
The enthalpy can be made into an intensive, or specific, variable by dividing by the mass. Engineers use the specific enthalpy in thermodynamic analysis more than the enthalpy itself. The specific enthalpy (h) of a substance is its enthalpy per unit mass. It equals to the total enthalpy (H) divided by the total mass (m).
h = H/m
h = specific enthalpy (J/kg)
H = enthalpy (J)
m = mass (kg)
Note that the enthalpy is the thermodynamic quantity equivalent to the total heat content of a system. The specific enthalpy is equal to the specific internal energy of the system plus the product of pressure and specific volume.
h = u + pv
In general, enthalpy is a property of a substance, like pressure, temperature, and volume, but it cannot be measured directly. Normally, the enthalpy of a substance is given with respect to some reference value. For example, the specific enthalpy of water or steam is given using the reference that the specific enthalpy of water is zero at 0.01°C and normal atmospheric pressure, where hL = 0.00 kJ/kg. The fact that the absolute value of specific enthalpy is unknown is not a problem, however, because it is the change in specific enthalpy (∆h) and not the absolute value that is important in practical problems.
See also: Steam Tables
Enthalpy of Vaporization
In general, when a material changes phase from solid to liquid, or from liquid to gas a certain amount of energy is involved in this change of phase. In case of liquid to gas phase change, this amount of energy is known as the enthalpy of vaporization, (symbol ∆Hvap; unit: J) also known as the (latent) heat of vaporization or heat of evaporation. Latent heat is the amount of heat added to or removed from a substance to produce a change in phase. This energy breaks down the intermolecular attractive forces, and also must provide the energy necessary to expand the gas (the pΔV work). When latent heat is added, no temperature change occurs. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.
Latent heat of vaporization – water at 0.1 MPa (atmospheric pressure)
hlg = 2257 kJ/kg
Latent heat of vaporization – water at 3 MPa (pressure inside a steam generator)
hlg = 1795 kJ/kg
Latent heat of vaporization – water at 16 MPa (pressure inside a pressurizer)
hlg = 931 kJ/kg
The heat of vaporization diminishes with increasing pressure, while the boiling point increases. It vanishes completely at a certain point called the critical point. Above the critical point, the liquid and vapor phases are indistinguishable, and the substance is called a supercritical fluid.
The heat of vaporization is the heat required to completely vaporize a unit of saturated liquid (or condense a unit mass of saturated vapor) and it equal to hlg = hg − hl.
The heat that is necessary to melt (or freeze) a unit mass at the substance at constant pressure is the heat of fusion and is equal to hsl = hl − hs, where hs is the enthalpy of saturated solid and hl is the enthalpy of saturated liquid.
Specific Enthalpy of Wet Steam
The specific enthalpy of saturated liquid water (x=0) and dry steam (x=1) can be picked from steam tables. In case of wet steam, the actual enthalpy can be calculated with the vapor quality, x, and the specific enthalpies of saturated liquid water and dry steam:
hwet = hs x + (1 – x ) hl
hwet = enthalpy of wet steam (J/kg)
hs = enthalpy of “dry” steam (J/kg)
hl = enthalpy of saturated liquid water (J/kg)
As can be seen, wet steam will always have lower enthalpy than dry steam.
A high-pressure stage of steam turbine operates at steady state with inlet conditions of 6 MPa, t = 275.6°C, x = 1 (point C). Steam leaves this stage of turbine at a pressure of 1.15 MPa, 186°C and x = 0.87 (point D). Calculate the enthalpy difference between these two states.
The enthalpy for the state C can be picked directly from steam tables, whereas the enthalpy for the state D must be calculated using vapor quality:
h1, wet = 2785 kJ/kg
h2, wet = h2,s x + (1 – x ) h2,l = 2782 . 0.87 + (1 – 0.87) . 790 = 2420 + 103 = 2523 kJ/kg
Δh = 262 kJ/kg