Humidity Measurement [Jan 2007]
Humidity is a property to which the human body itself responds
Background on humidity
The concept of humidity starts with basic thermodynamics.
According to the phase rule, for a system in phase equilibrium:
F = C – P + 2
where C = number of components, P = number of phases and F = number of degrees of freedom, that is, the number of intensive variables which can be changed without altering the number of phases. Further information on this can be found from standard texts on the subject. For liquid water in equilibrium with water vapour, C = 1 and P = 2 giving F = 1, so if one intensive variable is specified all of the others are fixed by nature. If we declare the temperature to be 100°C (373K) the pressure is fixed at 1 atmosphere (0.1 MPa) and this of course is the normal boiling point of water. If at this pressure we raise the temperature the liquid phase disappears, whereupon:
C = 1, P = 1 → F = 2
The vapour is then said to be superheated, meaning it is not in phase equilibrium with liquid and both pressure and temperature can be arbitrarily specified, therefore superheated vapour requires two intensive variables, in practice pressure and temperature, in order to specify it. Steam tables are used both for the saturated (F = 1) and superheated (F = 2) cases, for example in the operation of a steam turbine.
Another important way in which classical thermodynamics relates to the concept of humidity is that the Clausius-Clapeyron (C-C) equation applies. In fact the C-C equation applies to any phase equilibrium involving a single chemical substance. It does NOT apply to a mixture of more than one substance, therefore recent attempts to apply it for example to biodiesel are open to serious criticism.
In the area below is an application of the C-C equation to water in liquid/vapour equilibrium.
where P(Pa) = pressure, T(K) = temperature, ΔHvap(J mol-1) = heat of vaporisation and R = gas constant = 8.314 J K-1mol-1. We use a value of 43 J mol-1 for ΔHvap
the pressure is 105 Pa at the normal boiling point, 373K.
The above value for the vapour pressure at 70°C is in fact about 5% low; steam tables give it as 31160 Pa. The reason for the difference is that to take ΔHvap out of the integral is an approximation as the heat of vaporisation is itself a function of temperature and in a more rigorous treatment will be treated as such in application of the C-C equation, probably as a power series in temperature. Nevertheless, the C-C equation is often applied to vapour-liquid situations in the way it is in the above calculation, with a single value of the heat of vaporisation. This is so not only for water but for organic vapours. In this regard it should be noted that the term humidity can be extended to include any chemical compound where liquid and vapour co-exist. It is quite correct to talk about the humidity of for example benzene vapour in nitrogen in the total absence of water.
Whether the vapour/liquid co-existence is aqueous or non-aqueous, the relative humidity is the actual vapour pressure as a percentage of the equilibrium vapour pressure at the same temperature. The calculation that follows illustrates this.
If therefore the humidity of the room is measured as being 25%, that means that the actual pressure of water is:
Any humidity below 100% is therefore a non-equilibrium situation. There is only phase equilibrium when the vapour pressure is that calculated by the C-C equation. Is it possible for the humidity in a room to be above 100%? Yes, in principle and this too represents absence of phase equilibrium. In this event over time condensation will occur on walls and other surfaces in the room and phase equilibrium will be restored.
It is often necessary to be aware of the humidity of an area in which processing is taking place, notably in the textile and printing industries. Moreover, it is widely known that spontaneous combustion of coals and of cellulosic materials such as wood chips is exacerbated by moisture in the atmosphere so this necessitates knowledge of the humidity when such materials are stored or shipped. Humidity is of course very important in weather forecasting. Less well known is that the performance quality of a musical instrument can be affected by the humidity. These are amongst the reasons why methods of measuring humidity have been developed and these will be reviewed below.
Methods of measuring humidity
Classical methods
It was mentioned in the previous section that humidity measurement is important in the textile industry. Conversely, the action of moisture on a fibre material can be used as a basis for measuring humidity. The fibre material most commonly used for this purpose is human hair which, like wool, contains the fibre protein keratin. At high humidity such a fibre material extends along its length, the opposite occurring at low humidity. A suitably calibrated an assembly of strands of human hair stretched across two reference points constitutes a hair psychrometer. The usual arrangement is that at right angles to a vertical axis joining the two reference points is a thin strip of metal with a pen on the end. This contacts a rotating cylinder, enabling a continuous record of humidity to be obtained. Such devices, though classical, are still on the market in 2007. Two related points of scientific interest should be noted. First, moisture ‘uptake’ or ‘regain’ is a well known effect in wool technology. Secondly, one benefit of blow-drying one’s hair is that elongation of the fibres due to moisture gain, leading to a straggly appearance, is eliminated.
A sling psychrometer consists of two mercury-in-glass thermometers mounted a centimetre or so apart in a device whereby the pair of them can be rotated by hand. One has its bulb exposed to atmospheric air. The other has its bulb surrounded by a wick which has been saturated with water. The instrument is whirled, and water evaporates from the wick requiring the heat of vaporisation to do so, therefore a temperature drop is recorded at the thermometer. The other thermometer, the bulb of which is in air, reads room temperature. There will therefore be a difference between ‘wet bulb’ and ‘dry bulb’ temperatures. This difference and the room temperature constitute a data pair from which, by consultation of a table, the humidity can be deduced. For example, at 30°C a humidity of 5% is indicated by a difference of 18°C between the two bulb temperatures and 44% humidity by 9°C. The higher the humidity the smaller the difference between wet- and dry-bulb temperatures. At any room temperature, if Humidity Measurement the humidity were 100% the dry bulb would be experiencing the same moisture environment as the wet one and there would be no difference at all between the two bulb temperatures. Like hair psychrometers, sling psychrometers remain in use in the early 21st Century.
Instrumentational methods
In the area below is some background on capacitance, necessary for an understanding of how an electronic device for measuring humidity works.
In a capacitor, also known as a condenser, energy is stored in an electric field between two parallel conducting surfaces having equal and opposite charges separated by a dielectric which might well be air. The quantity capacitance is charge stored per unit potential and is therefore expressed in C V -1, or equivalently in farads. For such a capacitor the capacitance C is given by
where A = area of each plate (m2), D = distance between the plates (m) and ε = permittivity of the dielectric (farad m-1).
If in a capacitor the dielectric is air, the capacitance will depend on the humidity. A capacitor can therefore be calibrated for capacitance against humidity of the air. In a humidity meter working along these principles the dielectric will be a porous solid, perhaps porous silicon. Entry of water into the pores of such a material raises its capacitance and this is the basis of the measurement of humidity. Water has a permittivity about an order of magnitude higher than that of solid dielectrics so entry of water into the pores causes major increases in the capacitance of the dielectric which, with a suitable transducer, can be converted to a humidity reading
There is ongoing R&D into porous materials for such use and also into transducer devices. Porous materials having found such application include, in addition to silicon, alumina and various ceramics. A number of patents appertaining to dielectrics for humidity meters have been filed. Accuracies of humidity meters of this sort are usually about 1% humidity, not 1% of the humidity; a humidity reading of 25% would therefore be (25 ± 1)%, or a percentage uncertainty of 4.
As well as porous materials, certain polymers have been used as the dielectric in humidity meters. With polymers uptake can involve imbibition, a process analogous to dissolving which causes the properties of the polymer including its capacitance to change. One polymer used in humidity measurement is polyether imide (PEI), introduced in the 1980s under the trade name Ultem and finding many applications; there are many others which an interested reader can obtain details of from the Web. Humidity meters of this type are small enough to be hand held. Research is ongoing, both into new dielectric materials and into transducers. Sometimes humidity meters measure not the change in capacitance of the dielectric due to moisture but the change in impedance. Here an alternating current is applied and the impedance measured by a device which, in its principles, works similarly to the simple Wheatstone bridge.
Conceptual comparisons instrumentational methods with classical
The table that follows summarises the classical and modern methods outlined in this article.
| Hair psychrometer | Elongation of fibre protein strands due to moisture uptake measured as tension |
| Sling psychrometer | Heat of vaporisation requirement at the wet bulb causing a drop in the thermometer reading |
| Capacitance humidity meter | Changes in the capacitance of a dielectric due to moisture entry |
| Impedance humidity meter | Changes in the capacitance of a dielectric due to moisture entry |
In both classical and modern methods the scientific basis is simple. What student of physics at first-year university level would doubt that the capacitance of a dielectric will change as a result of exposure to moisture? The difference is that very simple and ‘transparent’ readings using simple and familiar devices are all that are required for the hair and sling psychrometers whereas those based on changes in the properties of a dielectric require transducers as noted. There will be other components to such a humidity meter, including an analogue to digital converter. There is R&D into these as well as into the dielectric materials themselves.
Dew points
Often a humidity meter will, as a bonus, provide a value for the dew point. Requisite background on this is in the area below.
air is cooled. It is therefore temperature at
which the actual pressure becomes the saturated vapour pressure. Imagine
that the humidity of air at 30°C is measured as 60%. The saturated vapour
pressure of water at that temperature is 4242 Pa. If the
humidity is 60% the actual vapour pressure is therefore:
actual vapour pressure from tables by interpolation of from
the C-C equation. It is actually 295K, 22°C. If the
room previously at 30°C is cooled to 22° liquid water will start to appear.
Software enabling calculations of the type in the box above to be carried out can easily be incorporated into a humidity meter whereupon the user knows what extent of cooling of the atmosphere will be necessary for condensation of water to occur. Also, some humidity meters also contain a resistance temperature detector (RTD) whereby the temperature of the atmosphere the humidity of which is being measured is also determined. The RTD, which in general is more accurate than a thermocouple, also uses a Wheatstone Bridge measurement circuit.
Concluding remarks
Humidity is a property to which the human body itself responds. Reliable knowledge of humidity is important in many industrial and other situations as already indicated and just one more such situation will be mentioned. Humidity is relevant to the safety of marathon running as the body loses heat by perspiration less readily if conditions are humid, and local codes and practices might require that the humidity be measured at the commencement of the race. The author is unaware of whether there has ever been any litigation in relation to this. If so accurate measurement of the humidity would be a key factor.
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