J12 Heat

Change of aggregate state of substances through change of heat content

Weighing of a known vapour volume

The method of Dumas 1827 evaporates a small quantity of fluid in a balloon (with a pointed opening) of known volume v (0.1-0.25 l) at the instantaneous, that is, known pressure p, by means of a fluid bath of (by 15 - 20) higher temperature than that of the boiling point of the fluid to be examined (because the vapour is to be overheated).The thermometer gives the temperature t of the bath, that is, also of the vapour t in the balloon; after evaporation of the fluid and overheating of the steam, the balloon is closed by melting at the tip and weighed. The weight difference compared with the weight of the empty balloon yields the mass m of the vapour.

Measurement of vapour volume of a weighted fluid mass

In the Gay-Lussac method of 1812, improved by August Wilhelm von Hofmann 1818-1892 1867 (Fig. 406), the weighted mass m of the sample is placed in the vacuum of a graduated Torricelli-tube B in a small stoppered bottle g, which is allowed to rise in the mercury. The Torricelli-tube is surrounded by a pipe M, through which passes steam at a known temperature. The heating by the steam causes the stopper to be ejected from the bottle; the fluid then evaporates, is overheated and depresses the mercury column. The length of the column h yields the pressure p mm, the graduation of B the volume v, the temperature of the vapour in M, which is also that of the vapour in B, the temperature y; hence all quantities required for the computation of the vapour density are known. The method cannot be employed with substances, which affect mercury!

Measurement of vapour volume by displacement of air

In the most frequently employed method of Hofmann 1878, you weigh the substance to be evaporated (m) and place it in the instrument, shown in Fig. 407. As it evaporates, it displaces a certain volume of air from the instrument, which is equal to the volume of the steam formed, for which it had to make room at the same pressure and temperature. You measure this volume of air by catching the air as it is being displaced in a measurement cylinder (over water). This volume of air and the mass m allow to compute the density of the vapour without measurement of the temperature of the vapour, because it has displaced a quantity of air, which under the same conditions has a volume equal to its own volume.

Fig. 407 shows the equipment. (At the start, the measurment cylinder is not yet over the gas delivery tube a coming from b.) As soon as the temperature in b, which is heated from the fluid bath c (water, aniline, sulphur, etc.), has become stable - namely when there do not rise anymore air bubbles from a in the water, that is, the air in b no longer expands - d is opened, the weighted fluid (in a small, closed vessel) placed into the tube and d closed rapidly. You now push the measurement cylinder over the gas delivery tube a, in order to catch the air emerging immediately at the start of evaporation. You read off the graduation of the measurement cylinder the volume v of the air, displaced by the steam; the air is at room temperature t and the barometric pressure, which is reduced by the (to be converted into mm of mercury) pressure of the water column below it. You have then all information for the computation of the volume of air, which equals the volume of vapour at the pressure and temperature of the evaporation; the weight of the volume of vapour itself is known by weighing of the mass m.

Relationship between vapour density and molecular weight

Why does a knowledge of the density of a vapour yield its molecular weight? According to Avogadro's rule (justified by the kinetic gas theory), all gases have in equally large spaces equally many molecules, provided that the pressure and the temperature are the same. Hence, if equal volumes of gas (v cm) contain equally many molecules, then the masses of equal volumes of gas are related to each other as the masses of the gas molecules - one says: Like the molecular weights of the gases. Hence the ratio of the mass of v cm of a gas, the molecular weight of which is being sought, to the mass of v cm oxygen is:

mass of v cm of a gas/mass of v cm of oxygen = molecular weight of the gas/molecular weight of oxygen.

Dividing on the left hand side the numerator and denominator simultaneously by the mass of v cm air, you obtain

[(mass of v cm gas)/(mass of v cm air)]/[(mass of v cm oxygen)/(mass of v cm air)] = (molecular weight of gas)/ (molecular weight of oxygen.

The numerator of the fraction on the left hand side is the vapour density D, related to air (determined by one of the three methods above), the denominator is the density of oxygen, related to air 1.1042, whence

D/1.1042 = M/32, that is, M = 32D/1.1042 = 28.98D

and the required molecular weight of the gas is around 29D.

If you measure the density of vapour, you can then test the correctness of chemical formulae. If the measured density of a vapour differs greatly from the theoretical one, you become aware of the presence of chemical processes, which could hardly be discovered otherwise, as, for example, that, in contrast to the vapours of most non-metals all metal vapours are monatomic (except Sb and Bi), that the vapour of sulphur at about 1000 does not contain 2, but 6 atoms in a molecule, etc.

If you relate the density of a vapour to that of water instead of air, you must multiply the numbers for D by the density of air. You thus find the density of a gas at 0 and the pressure of 1 atm: d = D0.0012932 g/cm, that is, d = (M/32)1.10420.0012932 = M/22417 g/cm. The specific volume, that is, the volume of 1 g mass, is then v = 1/d = 22417/M cm/g. The volume of M g mass, that is, of the mass, determined by the molecular weight - a mol - is for every gas the same number, whence it follows that, taking the in most cases very small deviation from the law of Boyle-Mariotte into account, it is 22415 cm or 22.415 l. This volume, related to 0 and the pressure of 1 atm, that is, to the normal conditions, is called the normal molvolume.


The conversion from the fluid aggregate state to the gaseous one is not the only change a substance can experience by heat input. If the entire fluid has been converted into vapour in a closed vessel, further heat input causes, first of all, a temperature rise of the vapour, but eventually something new: Decomposition of the molecules (dissociation). For example, if a quantity of water has been converted totally by heat intake into steam, the gaseous water substance decomposes eventually on further heat input into its components: Oxygen and hydrogen. The heat input is used for the work, which is required to remove the chemical bond (due to their affinity) of oxygen and hydrogen. However, a gas does not have a definite dissociation temperature like a fluid has a definite boiling temperature, but dissociation starts at a certain launch temperature, becomes ever stronger up to a mean dissociation temperature, at which it is most lively, and then gradually succumbs until it ceases at the final temperature. The terms launch and final temperature only denote the approximate temperature bounds of clearly perceptible dissociation.

According to Nernst 1864-1941, at the pressure of 1 atm at 1700C, about 0.6%, at 2200C, about 4 % of all water molecules are dissociated. Following kinetic gas theory, we imagine dissociation to be the following process: When a molecule impacts on another one or the wall of the vessel, it is fragmented into its atoms. The higher the temperature of a gas, the more molecules will attain the kinetic energy required for fragmentation. This is in agreement with the fact that dissociation rises with rising temperature. Individual molecules can also reach at comparatively low temperatures such large velocities , the required kinetic energy and thereby fragmentation; in fact, the really occurrring kinetic energy of single molecules obeys the laws of chance, only the mean value of the kintic energies of all molecules is determined uniquely by the temperature. At the temperature t and the pressure p, a definite fraction of n molecules is always dissociated. For example, in steam, under those conditions, nx molecules of n molecules are dissociated, that is, only n - nx = n(1 - x) molecules H2O are present as well as nx molecules H2 and nx atoms O, which form immediately n/2x molecules O2. Hence there exist after dissociation instead of the initial n molecules n(1 - x) + nx + n/2x = n(1 + x/2) molecules. The quantity x is called the degree of dissociation. However, after there has been installed a certain degree of dissociation in the mixture of the gases H2O, H2 and O2 , the chemical conversions do not at all finish. Also then every water molecule fragments at a sufficiently strong impact into its atoms. However, simultaneously, if two water molecules and one oxygen molecule impact with sufficient strength, they combine into water. In the equilibrium state as many molecules fragment as form anew.

As you have to expect according to the kinetic gas theory, that already at room temperature several, if only a very few water molecules split, you conclude that also then water molecules must form. At room temperature, the final equilibrium state between these three gases is only possible when the hydrogen and oxygen have combined without residue into water. This appear to be contradicted by the fact that a mixture of oxygen and hydrogen does not at all convert under normal conditions into water. Reason: At room temperature, the compounding occurs very slowly; the reaction rate is very slow, (You can convert the mixture by an explosion type process by means of an electrical spark.)

You can pursue the course of dissociation of a substance indirectly by measurement of its vapour density. This depends on the averaged molecular weight of all molecues and this weight changes with the decomposition of the matter. - If the fission products in equilibrium pass the heat back to the outside, they rejoin. Ammonium chloride, on dissociation by heat in a closed container, decomposes into ammonia gas and hydrogen chloride gas; if the heat is withdrawn, they rejoin into ammonium chloride. Hydrogen and oxygen gases, which were separated by dissociation of steam, rejoin during (slow) cooling into water.

Because of its spontaneous return, dissociation is not readily observed. (The first observation was made by Grove 1811- 196 1847, a first detailed examination only by St. Claire Deville 1818-1881 1857.) But you can prove it by passing the dissociation products through a porous wall: As a consequence of the differing molecular weights, that is, also their density, they diffuse at different rates and thereby separate in as much as that after a certain time the substance on the one side of the porous wall contains more of the less dense (faster) dissociation product, that on the other side more of the denser (slowlier) product. For example, during dissociation of ammonium chloride, you discover that one part reacts alkaline, (the one with more NH3), the other acid (the one with more HCl).

Liquefaction of gases. Critical temperature

When gases are overheated vapours, it must be possible to convert them into their fluid state as soon as they have become saturated vapours by application of cooling or pressure. And indeed, this is what happens. Water vapour becomes water as soon as its volume becomes smaller than the space which it can just saturate at the prevailing temperature. This reduction of volume can be attained by compression of the vapour or reduction of its temperature. Once a steam is saturated, liquefaction starts immediately; if it is overheated, you must either cool it, so that it contracts and approaches the saturation limit, or forcibly compress it until it occupies a space smaller than that which it can just saturate; gases like hydrogen, air, etc. are never saturated at room temperature, that is, you must reduce their temperature before they can become fluid. One has succeeded eventually in the liquefaction of all gases, even the (until 1880) considered to be invincible, permanent gases like helium, air, hydrogen, oxygen, nitrogen, nitric oxide, carbon monoxide, marsh gas. In order to being back water steam into its fluid state, it is sufficient to cool or compress it. (At least at the temperatures which normally arise, but it can also be different.) Also for many gases the one or the other method will work. Faraday has even liquefied at less than atmospheric pressure merely by cooling to -110C the gases: chlorine, cyanogen, ammonia, hydrogen sulphide, hydrogen iodide, hydrogen bromide, nitrous oxide and cabonic acid; merely by pressure increase at temperatures somewhat below 0, he has liquefied olefiant gas, carbonic acid, nitrous oxide, hydrogen chloride, hydrogen sulphide, hydrogen arsenic.

But you cannot liquefy any gas at any temperature by raising the pressure sufficiently high. A number of permanent gases have even resisted at 3 600 atm (Natterer 1821-1901), although they become fluid at much smaller pressures (Louis P.Cailletet 1832-1913, R.P.Pictet 1857-1937, E.Wroblewski 1845-1888, Karol Stanislav Olszewski 1846-1915), provided you compress them at a temperature below their critical one (Thomas Andrews 1813-1885 1869). In fact, there is for every vapour a critical temperature limit, above which it cannot exist as saturated vapour independently of however large is the pressure and above which a gaseous substance can only exist as overheated vapour, as gas. However, vapours, the temperature of which does not exceed the critical one, you can always compress into a space which they will then saturate at that temperature. The saturation pressure at the critical temperature is called critical pressure, the state of the gaseous substance at the critical temperature and pressure its critical state.

Depending on whether you perform the experiment of Fig. 405 at a lower (higher) temperature, the longer (shorter) is the straigh segment of its curve of state. It disappears at a certain temperature, the curve then starts to assume the shape of a hyperbola. This is the critical temperature. Fig. 408 presents the curves of state for carbonic acid at different temperatures. The dotted line is the upper bound of the region, in which it can exist partly gaseous, partly fluid; the coordinates of the highest point are the critical pressure and temperature.

For carbonic acid, the critical temperature is 31C, the saturation pressure about 73 atm. The critical temperature of sulphurous acid lies at + 157C; this acid, which is gaseous at normal temperature (boiling point -10C) can already become fluid at normal temperatures by a pressure of 1 - 2 atm. The critical temperatures are:

helium   hydrogen   oxygen   nitrogen
-268C   -240C   -119C   -147C

Water steam can be saturated at very high temperatures by pressure only. Its critical temperature is 374C, its critical pressure 224.2 atm.

Recently (in 1935), Benson has succeded in exploiting the behaviour of water at its critical point technically for the generation of high pressure steam of 150 atm and beyond: He pressurizes the water at 224.2 atm by means of a pump. The boiler comprises a system of spiral tubes, through which the water flows. The heat input through their walls raises the temperature of the water from below critical pressure to 374C. At this temperature, it transits without boiling up at increasing space addition into steam. Hence you save - it is one of the great advantages of the method - the evaporation heat! You must place a definite amount of water into the tube and the heat input carefully adjust to the evaporation heat. Just ahead of the critical point, the steam is in a labile state, a minute throttling would immediately separate 40 - 50% water. Hence you overheat the steam to 400C and then throttle it down to the required tension (100 - 200 atm).

In order to liquefy gases, you require a special tool for raising the pressure and lowering the temperature. Charles Cagniard de la Tour 1777-1859 and also Faraday has produced gases for liquefaction chemically in strong-walled glass tubes; in the process, the gases underwent very high pressure and eventually became liquid. Very high pressures are produced by compression pumps; in order to produce fluid and solid carbonic acid for technical purposes, the gas is pumped into a wrought-iron, strong-walled bomb. When the saturation pressure is reached (at 15C about 50 atm, at 20C 57 atm), the excess carbonic acid still pressed into the bomb is liquefied, because the space is saturated. When the bomb is separated from the compression pump and opened up, the fluid carbonic acide, exposed solely to atmospheric pressure, evaporates so fast that part of it becomes solid, because it takes the heat, it requires for evaporation, out of its own heat supply. If you let it in the process pass through a sieve like vessel, the solid carbonic acid collects in it. It is a snow-white mass; fluid carbonic acid is as clear as water (at 15C, its specific weight is 0.86). Solid carbonic acid (boiling point - 78.5C) evaporates in air only slowly; if you pour ether at room temperature over it, it evaporates strongly cooling the liquid. If the vapour is removed by an air pump and evaporation thereby fastened, the temperature drops to about -115C.

Louis P.Cailletet 1832-1913 1877 has employed a similar trick as the one to convert liquid carbonic acid into solid one for the liquefaction of oxygen, carbon monocide, nitrogen, air and hydrogen. He compresses them to 200 - 300 atm and then suddenly exposes them to atmospheric pressure. During the resulting enormous increase in volume and performed work, they cool so strongly, that they become liquid. Even further went R.P.Pictet 1857-1937 1878 by a cascade method: A gas (SO2), liquified by pressure and cold, precools a second more difficult to condense gas (CO2), which during liquefaction by pressure and cold reaches a considerably lower temperature (-140C) than the liquefaction temperature of the first gas (-65C). The second, liquefied gas precools a third, even more difficult to condense gas, etc. However, all of these processes yielded only quantities of fluid of the order of cm.

Liquefaction of gas by throttle cooling (Carl von Linde 1842-1934)

This process is quite different and allows to liquefy air in large quantities (0.75 - 100 l/hour); it employs the Joule-Thomson effect. If you throttle atmospheric air, as has been described, starting from the initial pressure p1 and temperature T1, and let the air after the throttle location depressurize, its cooling DT is as shown in the following table (Linde Jubilee volume, 1929):

T1   t1(C)   DT at p1=50 atm   DT at p1=100 atm   DT at p1=200 atm
288   15   11.6   22.5   39.0
253   -20   16.0   30.8   55.0
223   -50   21.4   42.7   71.5

The connection between, on the one hand, DT and, on the other hand, the starting temperature and the pressure difference before and behind the throttle valve have elucidated completely the investigation, required for gas liquefaction. It is much more complicated than what the Joule-Thomson formula expresses.

If you were to throttle down, according to this table, at room temperature (15C) starting from 200 atm to atmospheric pressure, the cooling of 39C without any other auxiliary means would be inconsequential for the liquefaction of the air. By introduction of the counter current cooler (in other words: Heat exchange between two air currents, moving past each other in opposite directions, Fig. 409) Linde succeeded. The counter current cooler works as follows: The densified air is cooled on its path to the throttle valve by depressed cold air, which travels in the opposite direction, whence its decompression starts already at a lower temperature. Also the temperature behind the depression valve is lowered hereby with consequent repeated colder cooling of the compressed air. The temperatures before and after the decompression valve must therefore drop further until eventually the air partly liquefies during decompression. The simplest arrangement for the execution of Linde's method is shown in Fig. 409. Until liquefiction starts, the same air circulates through the system of tubes; then a second pump introduces new, compressed air, in order to replace the liquefied part. After a certain time, a stationary state is established, because equlibrium occurs between the lowering of the temperature, induced by unavoidable heat intake from outside and the release of heat during the liquefaction. In this stationary state, the liquid air forms at O in quantities, which depend on the size of the machine (between 0.75 l/hour and 100 l/hour). The work input - in the most favourable case (Linde Jubilee volume) 2.86 PS hours/kg liquid air at 15C and decompression drom 200 to 1 atm - is reduced by two means:

1. The refrigerating capacity is approximately proportional to the pressure difference p2 - p1 at the throttling valve, in contrast the work input only depends on p2/p1, whence the refrigerating capacity is nearly the same wether you throttle from 150 to 1 atm or from 200 to 50 (high pressure cycle), the work input, however, is reduced to 28% of the value in the first case. By raising the lower pressure p1, the work input per kg liquid air can be reduced considerably. (With the high pressure cycle, you can achieve 1.53 PS hour/kg liquid air.)

2. The Joule-Thomson effect increases with dropping temperature. This fact can be exploited to increase the refrigerating capacity by lowering in a refrigerating machine the entrance tmperature into the counter current cooler, that is, by precooling the air. If it is precooled to - 50C, the Joule-Thomson effect and the refrigerating capacity are about twice as large as at an entrance temperature of + 15C. [With the simple decompression (200 atm to 0 atm) and precooling to - 50C, the work required is 1.378 PS hour/kg liquid air, with the high pressure cycle (between 200 and 50 atm) and precooling 0.905 PS hour/kg.]

The Linde process allows to liquefy air without precooling, but not hydrogen, because it becomes warmer in the Joule-Thomson effect at ordinary temperatures (inversion temperature - 80C). Its liquefaction only becomes possible (James Dewar 898) when you precool it by liquid air after compression prior to decompression. Liquid hydrogen boils in the atmosphere at - 253C. If you reduce the pressure on it, you can reach temperatures of - 264C. Also Helium can only be liquefied by Linde's method, when it is strongly precooled, since it heats in the Joule-Thomson effect (inversion temperature - 243C) at room temperature and even still at the temperature of liquid air (-190C). Helium boils in the atmosphere at -269C. By reduction of its vapour pressure, Onnes was able to reach 272.38C. [Hitherto, in 1935, de Haas reached in July 1933 by other means a temperature of only 0.085 above the absolute zero.]

You store liquefied gases in double-walled containers (Fig. 410) made out of glass or metal (Weinhold, Dewar). The space in between the walls is a vacuum and the walls are reflective, in order to exclude heat exchange by conduction and radiation between the fluid and its environment. In these vessels, the narrowed part for which does not favour evaporation, liquid air remains fluid for hours even at atmospheric pressure, although its temperature is - 190C. Out of the open bottle with liquid air evaporates more nitrogen (boiling point - 183C, whereby the liquid air gradually becomes richer in oxygen). In 100 % of the evaporaion residue are 23 % oxygen, in contrast in 90 % 37.5 %, in 10 % even 77 % oxygen. You separate the components of liquid air systematically from each other by different methods, which rely on the physical behaviour of mixtures of fluids (rectification, fractionated evaporation, fractionated condensation). Liquid air, liquid oxygen and liquid nitrogen are employed because of their low temperatures. But one also uses rare gases (discovered by Sir William Ramsay and John William Rayleight in 1895). 1 m of air contains 9.3.l argon, 15 cm neon, 5 cm helium, 50mm crypton, 6mm Xenon. Argon; Neon and Helium can be obtained in sufficient quantities. Argon is now used in large quantities in candescent lamps, in order to reduce the atomization of the wire. Neon is employed in neon tubes .


Since fluids transform into vapours through heat input and vapours through heat loss into fluids, you can separate fluids by sufficient heat input from solids, for example, those dissolved in them (like salt in water); moreover, in general, since different fluids boil at different temperatures, you can separate by heat input from each other the fluids in a mixture, since those boiling earliest will vapourize and those harder to vapourize will follow in due course depending on their boiling points. This process of separation is called distillation. Its execution demands essentially three components (Fig. 411):

1. A vessel A above a source of heat for the mixture, the retort,
a vessel B for the distilled fluid, the
a connecting tube C, through which the vapours rising in the retort flow to the receiver and into the
cooler, where they are reliquified by external cooling.

The temperature of of a mixture of fluids (a solution), which is required to start distillation depends on the nature of the fluids and the mixing ratio (the concentration of the solution). A mixture of alcohol and water boils already at 83C, if it contains 66% alcohol, and only at 90C if it only contains 10%. Water with 8 % cooking salt boils at 101C and with 40% only at 108 %, etc. During distillation, the composition of a fluid changes in the retort: In general, a solution becomes more concentrated and a mixture poorer in more readily evaporated fluid, whence the temperature of distillation rises. - During the distillation of a mixture, its components evaporate at different rates, whence the distillate consist mainly of the more volatile fluids, but it can also contain much of the substances which are harder to evaporate. You can complete the separation by repeated distillation. - Distillation is important for the fabrication of spirit, tar, etc. the equipment of which demands special lay outs (column apparatus).

Like distillation, sublimation also serves as a chemical working method, but with the difference that only such substances are suitable for sublimation (at normal pressure) which already have below their melting temperature considerable vapour pressures. You employ sublimation to separate solid substances of different volatility, frequently therefore for cleaning substances. The appropriate apparatus differs from that for distillation since the sublimate (condensate) precipitates as a solid.

Technical applications of liquefaction heat and evaporation cold

The liquifaction heat of steam is used technically for food preparation. Steam at 100C condenses as it enters colder water; the heat which is freed in this way heats up the water until its temperature has become that of the steam; at that stage, the steam exits. - It is just the same in the preheater of the steam boiler: The steam, which leaves a steam engine, flows (when the machine does not work with condensation) into the water of the preheater and heats it before it reaches the boiler. - Steam heating employs heat which becomes available in the tubes of the condenser. In order to enlarge the area, from which heat radiates, you connect the tubes to special ribs. - The loss of temperature which occurs during evaporation is used in porous clay containers (alkarazzas); they become damp outside and the evaporation from the surface, which is large due to its porosity, keeps the vessel and water in it cool. - Cooling of your skin, covered with sweat or water, ether, etc, as it dries through evaporation , cooling of the atmosphere after rain, etc. have the same explanation. Evaporation is accelerated and thereby cooling increased, if you replace during evaporation saturated , that is, no more absorbing air by fresh air; this is the reason for the cooling effect of waving a fan, of an air stream which has come across a cooling fluid (a lake), etc.

Evaporating water demands so much heat (latent) that you can convert it into ice by making it boil under the bell of an airpump and having sulphuric acid absorb immediately the steam, in order to impede saturation of the space of the steam. You can also cause it to freeze in the cryophor (Wollaston) (Fig. 412). which only contains (air free) water and steam. If the one sphere (B) has been emptied completely of water and been surrounded by a freezing mixture, the steam condenses to water, whence the space B contains less steam than it can accept and the water in A evaporates so fast, in order to saturate it, that is is frozen by the cooling.

Atmospheric precipitation

Liquifaction of steam in the atmosphere causes precipitation, which either can deposit on Earth's surface or on solid obstacles (dew, hoarfrost, glazed frost) or form in the air and drop to the ground (rain, snow, sleet, hail). Due to enduring evaporation, steam rises into the atmosphere from the water on Earth. Hence steam is always one part of the atmosphere and, depending on the prevailing pressure and temperature conditions and the present wind, it contributes to its distribution; at a given location, it is present in varying quantities. The pressure displayed by the barometer is therefore the pressure, which the air and water steam exert together. As long as it can exist at one location in the air as steam, there will occur no precitipitation. In general, it is present in the atmosphere as overheated steam, its position in the air might at the present temperature contain more steam than it really does. However, if the temperature sinks far enough, it approaches that temperature, at which it becomes saturated by the present steam and smallest cooling then liquefies the stea, The temperature, at which this starts, is called the dew point. Depending on the quantity of present steam and on the rate, at which it becomes liquified, precipitation assumes a different form.

One of the causes for cooling is contact of the steam with cold objects; in this way, dew and hoarfrost arise during the night (in the same way as smooth glas or metal faces become coated as you take them from a cold room into a warm one). The cause of the formation of clouds and precipitation is almost exclusively adiabatic cooling as air rises. Fog forms wherever warm air passes over cold soil, cools and hence liquefies. As soon as the strength of the rising flow of air ceases to be sufficient to keep the water drops suspended in the air, they fall as rain drops (with diameters of 0.5 to 0.7 mm) at velocities of 0.5 - 0.8 m/sec. If the steam liquefies below 0C, hoar frost and snow form in triagonal ice crystals, in snow arranged in the form of stars (Fig. 413). The steam content at a given location of the atmosphere influences obviously the weather. This is why Meteorology measures the water steam content of the air, in order to find out how far away the present temperature is from the dew poin. Moreover, since the climatic conditions of a location depend on the prevailing air humidity and this parameter is of vital importance for living organisms, its measurement - Hygrometry - is also important for Hygiene.


What is the objective of hygrometery? We sense the air in a room without its steam content changing as dry or damp depending on wether temperature is high or low. The physical difference is: The room requires at a higher temperature more steam in order to become saturated than at a lower temperature; however, in both cases, it disposes only of the same quantity of steam. In other words: With this amount of steam, the room is at a higher temperature further away from saturation than at a lower one. This larger or smaller distance of the prevailing state from saturation generates the impression of dryness or humidity.

At 20C, in order to be saturated, the air can at most accept 17.13 g steam per 1 m, at 9C only 8.8g. However, for example, if it contains actually at 20C only 10g, but at 9C 8 g, the air at 20C is dry compared with that at 9C, although it contains absolutely speaking in the first case more steam. In the first case, it lacks for saturation 42%, in the second case 9%. The humidity in a room should therefore only be judged in terms of the percentage that is lacking for saturation. The goal of measurements is the determination of relative humidity, that is, the ratio of the present amount of steam f to the maximally possible steam f0 (at saturation). You can determine f by sucking a measured quantity of air , say, 1 m, with an aspirator through a tube, containing calcium chloride or phosphoric anhydride or concentrated sulphuric acid and then determining the incease in weight of the substance, which absorbs water. The weight yields the amount of steam f in grams, which was contained in 1 m; you obtain from tables f0, the amount of steam at saturation at that temperature in 1 m.

This method is very exact, but demands a lot of time. However, you need not measure f directly: The ratio of the present amount of steam to that during saturation is almost equal to the ratio of the present steam pressure to that at saturaion at the same temperature, that is, the fraction f/f0 equals d/d0, where d and d0 are the corresponding values for the steam pressure; the pressure of steam is much more readily determined by thants amount ! Again tables provide the steam pressure d0; ( they also mostly provide the associated amount of steam f); the steam pressure d, that is the prevalent steam pressure, is measured by finding the temperature, to which the room must be cooled so that the available quantity of steam is sufficient for saturation, that is, every further cooling precipitates water. The tables present the pressure of the steam which at this temperature, the dew point, is saturated. - Hygrometers, which rely on this principle, are called dew-point or condensation hygrometers.

The basic form of the dew-point hygrometer has that of John Frederic Daniell 1790-1845 (Fig. 414). A and B are two glass spheres, connected air tight by a tube; A is filled half with ether. The thermometer C states the air temperature, the thermometer in A the temperature of the ether. Theinstrument contains only ether and its vapour. During measurement, the sphere B is cooled by drops of ether which fall on its surface and evaporate (in order to increase the area of evaporation and to accelerate the process, you fold absorbant muslin around it); the vapour of ether in B condenses, the vapour pressure inside drops and the ether in A starts to evaporate and distill to B. The ether in A cools and with it the sphere; eventually, the sphere A becomes so cold, that the steam of the air precipitates on it. The temperature (read on A), at which condensation starts, is the dew point, that is, the temperature at which the present amount of vapour is just enough for saturation of the space, where it is located - the accuracy of the measurement depends on tiny amounts of mist being visible on the glass sphere. It is therefore partly gilded.(Daniell's instrument is now only of historical interest. Regnault and Allouard have improved it considerably.) The utilisation of the numbers obtained is clear from the preceding work. For example, if the air temperature is 15C, the hygrometer displays the dew point at 5C, you will find in the tables that saturated steam of 5C has 6.543 mm pressure, saturated vapout at 15C 12.788 mm. The fraction d/d0 = 6.543/12.788 = 0.5117.

(We recall: d/d0, the ratio of the pressures, measures the humidity of the air, because it equals f/f0, the ratio of the really present amount of vapour to the at the prevailing temeprature maximally possible quantity of steam.)

Since you are to state the present amount of steam related to the maximally possible one, you express them in percentages, that is, you call the maximally possible one 100 and then have

d/d0 =f/f0 = x/100, whence x = 100d/d0 = 100f/f0.

In the above example, the air contains 51.17% of the maximally possible quantity of steam. The most frequently employed hygrometer is the pyrometer of August (1795-1870), which employs a similar principle: A damp body is evaporated on its surface the faster, that is, it cools the faster in comparison to the prevailing air temperature, the drier is the air surrounding it. The psychrometer (Fig. 415) has two thermometers together (graduated in tenths of degrees), which in every respect agree with each other. The bowel of the one, B, is covered by muslin,which is kept moist by feeding it from C through a wick with distilled water. Due to the evaporation of the water, B has always a lower temperature than A, which shows the air temperature, and, in fact, the psychometric difference is the larger, the further the air is from its saturation state. Cooling continues until the saturation pressure of the evaporating water and the vapour pressure of the air are in equilibrium, that is, the damp thermometer reaches that temperature, at which the steam in the air just condenses. The two temperatures allow to compute the degree of humidity of the air in a similar manner to that used above. August's psychrometer has been improved by Assmann 1845-1918 1885; he added aspiration and an arrangement to remove the effect of radiation.

The effectiveness of other hydrometers rests on the hygroscopic properties of organic substances like degreased hair, catgut, etc., which lengthen as they absorb steam. In the hair hygrometer of de Saussure 1783 (Fig. 416), the change in the length of a degreased human hair h moves a pointer along an empirically calibrated scale. The hair acts hygrometrically due to the diffusion equilibrium between its water content and the water vapour content of its environment.

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