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The humidity of air or gases usually influences our life completely unnoticed. And yet weather, as we know it, is not possible without humidity.
Why humidity?
Humidity drives most of the observable weather phenomena starting with clouds via fog, rain to storms and finally to such dramatic weather phenomena as hurricanes. It is not possible to forecast the weather exactly without precise knowledge of humidity in all the layers of the atmosphere. Correct relative humidity is important for our well-being and health. An important reason for the significance of humidity in our daily life is the fact that water can exist at normal temperatures (-20 to 30°C) in all 3 physical conditions and mainly also the high conversion energy of water from one physical condition into another one. Water in the air in its gaseous state, i.e. humidity, can store very large amounts of energy and can release it again during conversion to the liquid state, rain. Due to its properties, water, as humidity in the air, stabilises our climate and prevents large extremes of temperature.
On the other hand, humidity of air or gas in many industrial processes is extremely undesirable and can disrupt complete manufacturing processes; in turn, a precisely defined relative humidity must prevail for other manufacturing processes. In principle, humidity is always present. The question is how much, and how can I measure it and influence it if necessary?
Water as part of the air
Air is a mixture of a range of gases, of which the most well-known are nitrogen (N2) and oxygen (O2). Other components are various inert gases such as argon (Ar) and helium (He), carbon dioxide (CO2) and traces of other gases. A list of the most significant components in natural air with their proportions by volume can be seen in Table 1.
According to Dalton’s Law, a gas mixture like air with the total pressure (p) behaves under ideal conditions as if each component of the gas occupies the given volume alone and thus exerts a partial pressure (pi). The total pressure of the gas mixture is the sum of the partial pressures of the gases in the mixture and can be written for air as: p N2 partial pressure of nitrogen N 2 p O2 partial pressure of oxygen O 2 whereby the partial pressures behave as the proportions by volume of the gas components of the air.
A further significant component of the air is water vapour, i.e. water in gaseous form. Just like the other components of the air, the water vapour contained in the air exerts a partial pressure and humid air can be considered as a mixture of dry air and water vapour. Thus the total pressure of the humid air is derived from the sum of the partial pressure of the dry air (pa) and the water vapour partial pressure (e) and we get:
There is a maximum water vapour partial pressure for a given temperature which cannot be exceeded. For explaining the matter, consider a closed container at a temperature (t) which is half-filled with water; there is air in the space above the surface of the water (see Fig. 2).
Based on the thermal energy of the water molecule, water will evaporate for as long until a partial pressure (ew) materialises in the air space above the surface of the water. This saturation pressure ew(t) is the maximum possible which can exist for a given temperature (t). Exceeding the saturation vapour pressure results immediately in condensation; while this pressure is not exceeded water is evaporated from the water surface for as long until the maximum possible saturation vapour pressure ew(t) is reached again.
Without a free water surface, a vapour partial pressure (e) between 0 and ew(t) will always materialise. The saturation vapour pressure relating to a free water surface ew(t) is only dependent on the temperature and is of core importance for all considerations about humidity. Similar considerations can also be made with regard to a free ice surface and the saturation vapour pressure above ice ei(t) is obtained for temperatures < 0°C. Very precise vapour pressure functions, which are however very complicated to handle, are found in the literature for description of the saturation condition of water vapour. Therefore, approximation functions, so-called Magnus functions, are mostly used for normal technical applications:
The Magnus functions have the important benefit that analytical inverse functions also exist. The disadvantage is that different parameter sets must be used depending on the air temperature.
Real gas behaviour of humid air
Up until now, humid air has been considered as ideal gas. However, the air actually behaves as real gas, which manifests itself, among other things, as a marginally increased saturation vapour pressure ew'(t) as compared with the ideal saturation vapour pressure ew(t). The following equation is given:
The correction or “enhancement” factor (f) specifies the behaviour of humid air as compared with a system in which only water and water vapour are considered (pure phase). At ambient pressure and room temperature, f is ~ 1.004 and can thus be disregarded for most practical applications. The f-factor increases with increasing system pressure and is approximately 1.03 at 1MPa.
Quantities of humidity of air
The humidity of air or gases in general can be described in the most diverse ways which has its advantages depending on the application case. The different quantities of humidity are all equivalent and can be calculated from each of the others, whereby it is usually still the air temperature which plays a decisive role. The humidity quantities can be roughly divided into the following groups:
- Quantities which set the water vapour in the gas volume considered in relation to the proportion of dry air
- Quantities which describe the absolute water vapour quantity in the gas volume considered
- Quantities which put the water vapour quantity in relation to the water vapour quantity for saturation
Basically, a few humidity quantities are enough to be able to describe sufficiently all the problems occurring in practice. The following properties are assumed:
- Air pressure p [hPa]
- Air temperature t [°C]
- Water vapour saturation pressure ew(t) [hPa]
- Water vapour partial pressure e [hPa], 0 = e = ew(t)
Dew point temperature td [°C]
The dew point temperature is the temperature to which humid air or gas must be cooled down with constant pressure so that condensation just starts to occur. The following equation is valid for the occurrence of condensation:
I.e. the water vapour partial pressure is the same as the saturation vapour pressure at the dew point temperature. The dew point temperature can be derived directly from the water vapour partial pressure (e) using the Magnus function.
Relative humidity Uw [%]
The relative humidity is generally the most well known humidity measurement quantity. The reason for this is that together with the room temperature it is the most important quantity for specifying a pleasant ambient climate and thus for wellbeing. In general the relative humidity describes moisture exchange processes of materials or also of people with their surroundings.
For the relative humidity, the water vapour partial pressure (e) is set in relation to the saturation vapour pressure (ew) for the temperature (t). The relative humidity is therefore a measurement of how far humid air is away from the saturation condition. We get:
This definition applies to the complete temperature range, i.e. the relative humidity according to the WMO (World Meteorology Organisation) convention is also related to the saturation state with regard to water for temperatures < 0°C.
For temperatures where t > 0 °C, the water vapour partial pressure (e) cannot exceed the saturation vapour pressure ew(t), thus the relative humidity can never be greater than 100%.
Water vapour density (absolute humidity) dv [g/m3]
The mass of the water vapour contained in a given gas volume is set in relation to the gas volume (V). The absolute quantity of water vapour is stated in g per m3 of the gas volume:
The water vapour density depends on the total pressure (p) as well as on the gas temperature (t) and is used primarily as a measurement quantity for industrial drying processes.
Specific enthalpy h [kJ/kg]
The specific enthalpy of humid air is basically not a humidity measurement quantity, but instead provides a measurement for the necessary energy to produce a specific humid air condition. The enthalpy is not an absolute quantity, but instead it is always stated only as energy difference from one state to another. The condition of dry air at 0 °C is the arbitrary point of origin. The specific enthalpy of humid air is derived from the total heat energy necessary in order to:
- heat 1 kg of dry air from 0 °C to t
- evaporate the necessary amount of water in the humid air
- heat the water vapour from 0 °C to t
The specific enthalpy is usually related to 1 kg of dry air. As the total mass of the given humid air is not 1 kg but 1+r kg, the specific enthalpy is often also designated as h(1+r). The specific enthalpy is derived as a function of the mixture ratio r [kg/kg] where:
c p a = 1.00545 kJ/kg specific heat capacity of dry air at constant pressure c pv = 1.85894 kJ/kg specific heat capacity of water vapour at constant pressure l w = 2500.827 kJ/kg specific latent heat (evaporation heat) of water
Mollier diagram
Mollier diagrams are used to enable the graphical solution of complex thermodynamic calculations. Fig. 3 shows a simple Mollier diagram as a t – r graph. Condition changes of humid air are curves in the Mollier graph, for example, a heating of humid air is a vertical straight line as the mixture ratio (r) does not change during the heating.
Humidity measurement methods
There are a large number of humidity measurement methods, equipment and sensors for measuring humidity. However, ultimately only a few methods and sensors have really established themselves and are available in large quantities. The description of the individual measurement methods is made without considering accuracy and system costs but rather according to historical perspectives.
Hair hygrometer (fibre hygrometer)
The length of degreased and specially treated organic or synthetic fibres (e.g. human hair) changes with the relative humidity as a result of its hygroscopic behaviour. The maximum relative change in length can be up to 2.5%. The widely distributed and known hair or fibre hygrometers are based on this effect. They are actually the oldest hygrometers and in use to this day in countless different versions for wide temperature ranges from less than 0°C to more than 100°C.
Psychrometer (dry and wet bulb hygrometer)
This is one of the first humidity measurement devices which meets an increased demand for measurement accuracy. It basically consists of two thermometers, one of which is kept moist using a moistened cotton stocking. When air with a defined humidity flows past both the thermometers, the dry thermometer measures the air temperature (t). Water evaporates onto the surface of the wet cotton stocking until the air flowing by reaches 100% relative humidity locally. The necessary energy for the evaporation of the water is taken from the wet thermometer which is thereby cooled down. Finally, an equilibrium temperature (tw) with the temperature of the air flowing by sets itself on the wet thermometer. The water vapour partial pressure (e) of the air flowing by is derived from:
With corresponding maintenance, psychrometers show a very good accuracy in the temperature range from 5 to 50 °C; the measurement errors increase significantly at higher and lower temperatures.
Chilled mirror hygrometer
A small mirror is purged with measuring gas and kept cooled down until the temperature falls below the dew point / frost point temperature and a coating layer forms on the mirror. This coating formation is detected optically whereby either the light directly reflected by the mirror is measured and a weakening in intensity is registered during coating formation or the diffused light produced by the coating is measured. The intensity and coating thickness are maintained using an electronic controller, the temperature of the mirror corresponds to the dew point temperature and frost point temperature respectively.
Al2O3 sensor
The measurement method is based on the adsorption of water vapour on a porous Al2O3 layer. The sensor is designed as a condenser and usually consists of a master electrode made of solid Al which the Al2O3 layer is applied to using anodic oxidation. A porous gold layer is arranged as the opposite electrode.
During the adsorption, the humidity-dependent capacity of the sensor changes due to the high dielectric constant of the accumulated water which represents a measure of the absolute humidity in first approximation for the sensor. The capacity change becomes smaller and smaller for low humidity; at the same time the accuracy of the measurement drops and the reaction time becomes larger and larger.
Capacitive polymer sensors
Of all the sensors available on the market for humidity measurement, the capacitive polymer sensors are by far the most successful. They are used with different designs and configuration options with great success in air conditioning technology and in the automotive industry. There are successful applications in industrial measuring technology, partly aggravated usage conditions, in agriculture and in meteorology. Extremely short reaction times at low temperatures are achieved with special design options so that usage in radio sondes at temperatures down to -80 °C is possible.
