# Enthalpy in practice

It is not possible to give an absolute value to enthalpy since no assessment is possible of the absolute value of the internal energy of a gas. The expression, mentioned earlier, of internal energy as a function of pressure and temperature, is a simplification. Fortunately, air conditioning involves only a calculation of changes in enthalpy. It follows that such changes may be readily determined if a datum level of enthalpy is adopted for its expression. Thus, we are really always dealing in relative enthalpy, although we may not refer to it as such.

The enthalpy, h, used in psychrometry is the specific enthalpy of moist air, expressed in kJ kg-1 dry air, defined by the equation:

H = ha + ghg (2.20)

Where ha is the enthalpy of dry air, hg is the enthalpy of water vapour, both expressed in kJ kg“1, and g is the moisture content in kg per kg dry air.

The value of temperature chosen for the zero of enthalpy is 0°C for both dry air and liquid water. The relationship between the enthalpy of dry air and its temperature is not quite linear and values taken from NBS Circular 564 (1955), for the standard atmospheric pressure of 101.325 kPa and suitably modified for the chosen zero, form the basis of the CIBSE tables of the properties of humid air. An approximate equation for the enthalpy of dry air over the range 0°C to 60°C is, however

/ia= 1.007*-0.026 (2.21)

And for lower temperatures, down to -10°C, the approximate equation is

Aa= 1.005* (2.22)

Values of /ig for the enthalpy of vapour over water have been taken from NEL steam tables (1964), slightly increased to take account of the influence of barometric pressure and modified to fit the zero datum. The enthalpy of vapour over ice, however, is based on Goff (1949).

For purposes of approximate calculation, without recourse to the CIBSE psychrometric tables, we may assume that, in the range 0°C to 60°C, the vapour is generated from liquid water at 0°C and that the specific heat of superheated steam is a constant. The following equation can then be used for the enthalpy of water vapour:

/zg = 2501 + 1.84* (2.23)

Equations (2.21) and (2.23) can now be combined, as typified by equation (2.20), to give an approximate expression for the enthalpy of humid air at a barometric pressure of

101.325 kPa:

H = (1.007* — 0.026) + #(2501 + 1.84*) (2.24)

EXAMPLE 2.10

Calculate the approximate enthalpy of moist air at a dry-bulb temperature of 20°C, 50 per cent saturation and a barometric pressure of 101.325 kPa. Use CIBSE psychrometric tables or a psychrometric chart to establish the moisture content.

From tables (or less accurately from a chart),

G = 0.007 376 kg per kg dry air

Using equation (2.24)

Ft = (1.007 x 20 — 0.026) + 0.007 376 x (2501 + 1.84 x 20)

= 38.83 kJ per kg dry air

CIBSE quote a value of 38.84 kJ per kg dry air.

For the range of temperatures from -10°C to 0°C equation (2.23) is also approximately correct for the enthalpy of water vapour over ice. Using equations (2.22) and (2.23) the combined approximate equation for the enthalpy of humid air over ice becomes

H = 1.0051 + g(2501 + 1.840 (2.25)

EXAMPLE2.il

Calculate the approximate enthalpy of moist air at a dry-bulb temperature of-10°C, 50 per cent saturation and a barometric pressure of 101.325 kPa. Use CIBSE psychrometric tables or a psychrometric chart to establish the moisture content.

From tables (or less accurately from a chart)

G = 0.000 804 kg per kg dry air

Using equation (2.25)

Ft = 1.005 x (-10) + 0.000 804(2501 + 1.84 x (-10))

= -8.054 kJ per kg dry air

CIBSE tables quote -8.060 kJ per kg dry air.

As in the case of specific volume, the general principle followed by ASHRAE (1997), Goff (1949) and CIBSE (1986) for determining the enthalpy of moist air is to add to the enthalpy of dry air, fta, a proportion of the difference between the enthalpy of saturated air, fts, and the enthalpy of dry air, fta. This is expressed by the following equation:

Ft = Aa + m(As — ft.)/100 (2-26)

Where (a, is the percentage saturation.

EXAMPLE 2.12

Calculate the enthalpy of moist air at a dry-bulb temperature of 20°C, 50 per cent saturation and a barometric pressure of 101.325 kPa using equation (2.26).

From CIBSE psychrometric tables (or, less accurately, from a psychrometric chart), the enthalpy of dry air, fta, is 20.11 kJ per kg dry air and the enthalpy of saturated air, fts, is 57.55 kJ per kg dry air. Hence, by equation (2.26):

Ft = 20.11 + 50(57.55 — 20.11)/100 = 38.83 kJ per kg dry air

CIBSE tables quote 38.84 kJ/kg dry air. The difference is due to rounding off.

EXAMPLE 2.13

Calculate the enthalpy of moist air at a dry-bulb temperature of 60°C, 50 per cent saturation and a barometric pressure of 101.325 kPa. Use CIBSE psychrometric tables to establish the moisture content.