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Physical Properties of Air
Main Physical Properties of Air are: tasteless and inodorous gas which appears colourless, except in very deep layers when a faint blue colour is visible, which has been attributed to its ozone content. Under normal conditions of 760 mm. pressure and 0° C., the weight of a litre of air varies, as a rule, between 1.2927 and 1.2933 grams, the variation being attributable to the fact that the air has not a perfectly constant chemical composition. For this reason it is useless to determine with great accuracy the density of a gas relatively to air unless the composition of the latter is simultaneously ascertained. For most purposes a mean value of 1.2930 at 0° C. and 760 mm. will be a sufficiently accurate figure to adopt. One gram of air under the above conditions will occupy 773 c.c., and its density with reference to hydrogen is 14.44. At 15° C. 1000 cubic feet of air weigh 76.5 lb., whilst 1 lb. of air occupies 13.07 cubic feet.
With a knowledge of the density of each constituent of the air it is possible to calculate the relative proportions of nitrogen and oxygen in the atmosphere; but such calculations at first indicated more oxygen than could be found by direct analysis, and not until the discovery of argon was the cause of the discrepancy realised. Knowing the density of oxygen, nitrogen, and argon, the proportion of these gases in the atmosphere can now be calculated to be as follows:
Calculation of composition of Air from density determinations
That the air possesses weight was apparently first recognised by Jean Rey, c. 1630, an observation that was confirmed by Torricelli in 1643 and by Pascal in 1648. Rey made his discovery by observing that tin, on calcination in air, increases in weight, and thus anticipated the results of Lavoisier by nearly a century and a half. Torricelli tackled the problem in an entirely different manner. He filled with mercury a glass tube, closed at one end and measuring some 3 feet in length. When the tube was inverted with its open end dipping under mercury in a trough, the tube no longer remained filled with the liquid. It held a column of mercury some 30 inches in height, but above this the tube was empty. This space came to be known as the Torricellian vacuum, and its discoverer correctly attributed its formation to the fact that the open air acting on the surface of the mercury in the trough is able to support by its pressure a column of mercury of definite length, and no more. Pascal extended Torricelli's experiments by employing tubes filled with other liquids such as oil, alcohol, and water. In every case he found that the height of the column of liquid supported by the air was inversely proportional to the liquid density; in other words, the pressure supported was constant, irrespective of the chemical composition of the liquid. Pascal also surmised that if air is a ponderable fluid, it will exert a greater pressure at sea level than on the top of a mountain, and that this difference should be capable of measurement by observing the relative heights of mercurial columns in such situations. Experiment proved this to be the case. Boyle christened Torricelli's tube, containing mercury, a barometer, and it is customary to express the pressure of the air in terms of the height of a column of mercury which it is capable of supporting at any moment.
The pressure of the air, as already mentioned, varies with altitude; indeed, at one and the same place it does not remain constant in consequence of variation in composition, the influence of wind, etc. A standard pressure, known as an atmosphere, has been chosen. The British unit is a column of mercury 29.905 inches in height, measured at 32° F. in London, and is equivalent to a pressure of 14.73 lb. per square inch.
The metric unit is a column of mercury 760 mm. (29.922 inches) in height measured at 0° C. at sea level at latitude 45°. The density of mercury at 0° C. is 13.596, and the acceleration due to gravity at sea level and,at latitude 45° is 980.60 cm. per sec. Hence the value of the metric standard of pressure is
76.0×13.596×980.60 = 1013250 dynes per sq. cm.
which is equivalent to a weight of 1033.3 grams per sq. cm. The British atmosphere is 0.99968 that of the metric unit.
Other Physical Properties of Air are given bolow:
The total weight of the atmosphere is approximately as follows:
Except at pressures but little removed from atmospheric, air does not obey Boyle's Law. Regnault, who was the first investigator to obtain trustworthy results, found that air deviated appreciably from the Law between pressures of 1 and 27 atmospheres- - the range used - the gas being more compressible than the Law demands. Several other investigators then took up the work, the most important experiments being those of Amagat, whose results are given in the following table, together with the data obtained by him for oxygen and nitrogen.
The results for oxygen and nitrogen are shown diagrammatically in fig. together with curves for hydrogen and carbon dioxide for the sake of comparison.
It will be observed that air gives results intermediate between those of nitrogen and oxygen, as is to be expected from a mixture of the two. At first the values for PV fall, the attraction between the molecules causing the gases to be more compressible than Boyle's Law demands. As, however, the pressure increases, the volume ceases to contract in strict proportionality, since the dimensions of the molecules themselves begin to make themselves felt. The gas thus becomes less compressible than the law demands.
As the temperature falls, air shows an ever increasing tendency to deviate from Boyle's Law. This is well demonstrated by the results of Witkowski given in the table and shown diagrammatically in Fig.
Relation between pressure and volume of oxygen, nitrogen and air
The mean specific heat of air at constant pressure rises with the temperature. The most reliable data are those given in the next table.
The variation of the specific heat at constant pressure over a range of 1 to 300 atmospheres is readily calculated for a mean temperature of 60° C. from the formula
104Cp = 2414 + 2.86p + 0.0005p2 - 0.0000106p3, where p represents the pressure in atmospheres.
The Compressibility of Air
The variation of the molecular heat at constant volume with rise of temperature between 0° C. and 700° C. is given by the expression
Cv = 4.8 + 0.0004T,
where T is the absolute temperature.
Partington gives the following results at 17° C.:
The ratio of the specific heat at constant pressure to that at constant volume is given by the expression
γ = Cp/Cv = 0.2387/0.1701 = 1.4027.
Other recent values for γ, as determined by different investigators, are between 1.400 and 1.4034:
These values agree well with that required theoretically for a diatomic gas.
The value for γ is stated to remain constant to within 1 per cent, between 0° and 500° C., although most observers agree that γ tends to fall with rise of temperature.
Increase of pressure, however, raises the value from 1.404 at 0.5 atm. to 1.411 at 3.5 atm., 1.460 at 20 atm., and 1.533 at 50 atm.
The coefficient of expansion of dry air, with rise of temperature per 1° C. and at normal pressure, has been variously determined as between 0.0036677 and 0.0036843.
For a gas that obeys Boyle's Law, the coefficient of expansion at constant pressure is the same numerically as the coefficient of pressure increase with rise of temperature at constant volume. The more important results obtained for this latter coefficient are as follow:
Pressure coefficient of Air
The coefficient of viscosity of air is given as 0.000180 at 11.75° C. The thermal conductivity of air at the mean temperature of 55° C. is 0.0000571, a value intermediate between that of oxygen (0.0000593) and nitrogen (0.0000569).
The velocity of sound in free air at various temperatures has been determined as follows:
The velocity of sound in free air as determined by the Bureau des Longitudes is 331.2 metres per second, whilst Hebb found the value 331.44, and Gruneisen and Merkel 331.57 at 0° C. and 760 mm.
The refractive index of dry air is 1.0002918 at 0° C. and 760 mm. for the sodium D line (λ = 5893×10-8 cm.); the indices for other wavelengths not widely removed may be calculated from Cauchy's equation
n - 1 = A(1 + B/λ2).
where n and A represent the refractive index and wave-length respectively, whilst A and B are constants of values 28.71×10-5 and 5.67×10-11 respectively. The latter constant B is the coefficient of dispersion. According to Cuthbertson the refractive index n of air for any incident light of frequency f is given by the expression
For the sake of comparison, the refractive indices of the more important individual gases present in the atmosphere are given in the following table:
When entirely free from dust, dry air possesses a high degree of transparency to light, which the presence of moisture and dust tends to decrease. This is evident from the following table:
Dry air is highly diathermanous, that is to say, it absorbs but little of the sun's heat.
Owing to its oxygen content, air is magnetic, its magnetic susceptibility being about 0.25×10-7 at 10° C.
Its specific inductive capacity or dielectric constant referred to a vacuum is 1.000586 at 0° C., and 1.000576 at 20° C.
The solubility of air in water has been made the subject of considerable research, and possesses several points of interest. The independence of the two main constituents (argon being included with the nitrogen) is clearly observable from the table given below; further, owing to the fact that the coefficients of solubility of the individual gases are affected differently with rise of temperature the composition of the dissolved mixture is not constant.
Since oxygen is practically twice as soluble in water as nitrogen, it follows that the dissolved gas is proportionately richer in oxygen. By expelling the gas into a vacuum and reabsorbing it in water, the concentration of the oxygen is still further increased. By repeating these processes several times, a fairly pure oxygen can be obtained, and this has been made the basis of a patent for the commercial separation of oxygen from the air.
The number of cubic centimetres of oxygen and nitrogen (containing argon) dissolved in a litre of water saturated with air from a dry atmosphere at 760 mm. pressure at various temperatures are given in the following table:
Solubility of Air in Water at various temperatures
Measurement has also been made of the solubility of air in sulphuric acid of varying concentration. At 18° C. the coefficient of solubility in 98 per cent, acid is 0.0173, and in 70 per cent, acid attains a minimum value of 0.0055.
With a knowledge of the density of each constituent of the air it is possible to calculate the relative proportions of nitrogen and oxygen in the atmosphere; but such calculations at first indicated more oxygen than could be found by direct analysis, and not until the discovery of argon was the cause of the discrepancy realised. Knowing the density of oxygen, nitrogen, and argon, the proportion of these gases in the atmosphere can now be calculated to be as follows:
Calculation of composition of Air from density determinations
| Weight per cent. | Volume per cent. | |
| Oxygen | 23.2 | 21.00 |
| Nitrogen | 75.5 | 78.06 |
| Argon | 1.3 | 0.94 |
That the air possesses weight was apparently first recognised by Jean Rey, c. 1630, an observation that was confirmed by Torricelli in 1643 and by Pascal in 1648. Rey made his discovery by observing that tin, on calcination in air, increases in weight, and thus anticipated the results of Lavoisier by nearly a century and a half. Torricelli tackled the problem in an entirely different manner. He filled with mercury a glass tube, closed at one end and measuring some 3 feet in length. When the tube was inverted with its open end dipping under mercury in a trough, the tube no longer remained filled with the liquid. It held a column of mercury some 30 inches in height, but above this the tube was empty. This space came to be known as the Torricellian vacuum, and its discoverer correctly attributed its formation to the fact that the open air acting on the surface of the mercury in the trough is able to support by its pressure a column of mercury of definite length, and no more. Pascal extended Torricelli's experiments by employing tubes filled with other liquids such as oil, alcohol, and water. In every case he found that the height of the column of liquid supported by the air was inversely proportional to the liquid density; in other words, the pressure supported was constant, irrespective of the chemical composition of the liquid. Pascal also surmised that if air is a ponderable fluid, it will exert a greater pressure at sea level than on the top of a mountain, and that this difference should be capable of measurement by observing the relative heights of mercurial columns in such situations. Experiment proved this to be the case. Boyle christened Torricelli's tube, containing mercury, a barometer, and it is customary to express the pressure of the air in terms of the height of a column of mercury which it is capable of supporting at any moment.
The pressure of the air, as already mentioned, varies with altitude; indeed, at one and the same place it does not remain constant in consequence of variation in composition, the influence of wind, etc. A standard pressure, known as an atmosphere, has been chosen. The British unit is a column of mercury 29.905 inches in height, measured at 32° F. in London, and is equivalent to a pressure of 14.73 lb. per square inch.
The metric unit is a column of mercury 760 mm. (29.922 inches) in height measured at 0° C. at sea level at latitude 45°. The density of mercury at 0° C. is 13.596, and the acceleration due to gravity at sea level and,at latitude 45° is 980.60 cm. per sec. Hence the value of the metric standard of pressure is
76.0×13.596×980.60 = 1013250 dynes per sq. cm.
which is equivalent to a weight of 1033.3 grams per sq. cm. The British atmosphere is 0.99968 that of the metric unit.
Other Physical Properties of Air are given bolow:
The total weight of the atmosphere is approximately as follows:
| Tons. | |
| Nitrogen (including argon, etc.) | 4,041,200,000,000,000 |
| Oxygen | 1,218,040,000,000,000 |
| Carbon dioxide | 3,156,000,000,000 |
Except at pressures but little removed from atmospheric, air does not obey Boyle's Law. Regnault, who was the first investigator to obtain trustworthy results, found that air deviated appreciably from the Law between pressures of 1 and 27 atmospheres- - the range used - the gas being more compressible than the Law demands. Several other investigators then took up the work, the most important experiments being those of Amagat, whose results are given in the following table, together with the data obtained by him for oxygen and nitrogen.
 |
| The compressibilities of oxygen and nitrogen (Amagat, 1893) |
It will be observed that air gives results intermediate between those of nitrogen and oxygen, as is to be expected from a mixture of the two. At first the values for PV fall, the attraction between the molecules causing the gases to be more compressible than Boyle's Law demands. As, however, the pressure increases, the volume ceases to contract in strict proportionality, since the dimensions of the molecules themselves begin to make themselves felt. The gas thus becomes less compressible than the law demands.
 |
| The compressibility of air (Witkowski, 1896). |
Relation between pressure and volume of oxygen, nitrogen and air
| Pressure in Atm. | PV at 0° C. (Oxygen). | PV at 0° C. (Nitrogen). | PV at 0° C. (Air). |
| 1 | 1.0000 | 1.0000 | 1.0000 |
| 100 | 0.9265 | 0.9910 | 0.9730 |
| 200 | 0.9140 | 1.0390 | 1.0100 |
| 300 | 0.9625 | 1.1360 | 1.0975 |
| 400 | 1.0515 | 1.2570 | 1.2145 |
| 500 | 1.1570 | 1.3900 | 1.3400 |
| 1000 | 1.7360 | 2.0700 | 1.9990 |
| 1500 | 2.2890 | 2.72025 | 2.6310 |
| 2000 | 2.8160 | 3.3270 | 3.2260 |
| 2500 | 3.32375 | 3.9200 | 3.79125 |
| 3000 | 3.7120 | 4.4970 | 4.3230 |
The mean specific heat of air at constant pressure rises with the temperature. The most reliable data are those given in the next table.
The variation of the specific heat at constant pressure over a range of 1 to 300 atmospheres is readily calculated for a mean temperature of 60° C. from the formula
104Cp = 2414 + 2.86p + 0.0005p2 - 0.0000106p3, where p represents the pressure in atmospheres.
The Compressibility of Air
| Pressure.(Atm.) | Values for PV at | |||||
| -140° C | -130° C | -78.5° C | 0° C | +16° C. | +100° C. | |
| 1 | 0.4862 | 0.5229 | 0.7119 | 1.0000 | 1.0587 | 1.3670 |
| 10 | . . . | . . . | . . . | 0.9951 | 1.0550 | 1.3678 |
| 20 | 0.3808 | 0.4410 | 0.6778 | 0.9897 | 1.0509 | 1.3691 |
| 30 | 0.3063 | 0.3936 | 0.6599 | 0.9842 | 1.0468 | 1.3704 |
| 40 | 0.1128 | 0.3329 | 0.6423 | 0.9793 | 1.0433 | 1.3725 |
| 50 | . . . | 0.2544 | 0.6252 | 0.9754 | 1.0408 | 1.3754 |
| 60 | . . . | 0.2013 | 0.6089 | 0.9723 | 1.0390 | 1.3784 |
| 70 | . . . | 0.1989 | 0.5937 | 0.9701 | 1.0381 | 1.3821 |
| 80 | . . . | 0.2043 | 0.5796 | 0.9688 | 1.0379 | 1.3866 |
| 90 | . . . | . . . | 0.5680 | 0.9681 | 1.0382 | 1.3908 |
| 100 | . . . | . . . | . . . | 0.9681 | 1.0390 | 1.3951 |
| 110 | . . . | . . . | . . . | 0.9690 | 1.0406 | 1.4004 |
| 120 | . . . | . . . | . . . | 0.9710 | 1.0432 | 1.4065 |
| 130 | . . . | . . . | . . . | 0.9738 | 1.0467 | . . . |
The variation of the molecular heat at constant volume with rise of temperature between 0° C. and 700° C. is given by the expression
Cv = 4.8 + 0.0004T,
where T is the absolute temperature.
Partington gives the following results at 17° C.:
| Specific heat at constant volume | 0.1701 |
| Specific heat at constant pressure | 0.2387 |
| Molecular heat at constant volume | 4.931 |
| Molecular heat at constant pressure | 6.920 |
The ratio of the specific heat at constant pressure to that at constant volume is given by the expression
γ = Cp/Cv = 0.2387/0.1701 = 1.4027.
Other recent values for γ, as determined by different investigators, are between 1.400 and 1.4034:
These values agree well with that required theoretically for a diatomic gas.
The value for γ is stated to remain constant to within 1 per cent, between 0° and 500° C., although most observers agree that γ tends to fall with rise of temperature.
Increase of pressure, however, raises the value from 1.404 at 0.5 atm. to 1.411 at 3.5 atm., 1.460 at 20 atm., and 1.533 at 50 atm.
The coefficient of expansion of dry air, with rise of temperature per 1° C. and at normal pressure, has been variously determined as between 0.0036677 and 0.0036843.
For a gas that obeys Boyle's Law, the coefficient of expansion at constant pressure is the same numerically as the coefficient of pressure increase with rise of temperature at constant volume. The more important results obtained for this latter coefficient are as follow:
Pressure coefficient of Air
| Pressure. cm. Hg. | Temperature, Range, ° C | Co-efficient of Pressure. |
| 0.58 | . . . | 0.0037666 |
| 1.32 | . . . | 0.0037172 |
| 10.0 | . . . | 0.0036630 |
| 17-24 | . . . | 0.0036513 |
| 23 | 0-1067 | 0.0036643 |
| 76 | . . . | 0.0036650 |
| 100.1 | 0-100 | 0.0036744 |
| 200 | . . . | 0.003690 |
| 2000 | . . . | 0.003887 |
The coefficient of viscosity of air is given as 0.000180 at 11.75° C. The thermal conductivity of air at the mean temperature of 55° C. is 0.0000571, a value intermediate between that of oxygen (0.0000593) and nitrogen (0.0000569).
The velocity of sound in free air at various temperatures has been determined as follows:
| Temp., ° C | 0/td> | 100 | 200 | 300 | 400 | 500 | 600 | 700 |
| Velocity, m. per sec | 331.8 | 387.5 | 435.8 | 479.0 | 518.6 | 555.2 | 589.3 | 621.6 |
The velocity of sound in free air as determined by the Bureau des Longitudes is 331.2 metres per second, whilst Hebb found the value 331.44, and Gruneisen and Merkel 331.57 at 0° C. and 760 mm.
The refractive index of dry air is 1.0002918 at 0° C. and 760 mm. for the sodium D line (λ = 5893×10-8 cm.); the indices for other wavelengths not widely removed may be calculated from Cauchy's equation
n - 1 = A(1 + B/λ2).
where n and A represent the refractive index and wave-length respectively, whilst A and B are constants of values 28.71×10-5 and 5.67×10-11 respectively. The latter constant B is the coefficient of dispersion. According to Cuthbertson the refractive index n of air for any incident light of frequency f is given by the expression
For the sake of comparison, the refractive indices of the more important individual gases present in the atmosphere are given in the following table:
| Gas or Vapour. | n for D line. |
| Air | 1.0002918 |
| Argon | 1.0002837 |
| Nitrogen | 1.000297 |
| Oxygen | 1.000272 |
| Water-vapour | 1.000257 |
When entirely free from dust, dry air possesses a high degree of transparency to light, which the presence of moisture and dust tends to decrease. This is evident from the following table:
| Coefficient of Transparency. | |
| Dry, dust free air | 0.99718 |
| Moist, dust free air | 0.99388 |
| Air in a dusty dwelling-house room | 0.9952 |
Dry air is highly diathermanous, that is to say, it absorbs but little of the sun's heat.
Owing to its oxygen content, air is magnetic, its magnetic susceptibility being about 0.25×10-7 at 10° C.
Its specific inductive capacity or dielectric constant referred to a vacuum is 1.000586 at 0° C., and 1.000576 at 20° C.
The solubility of air in water has been made the subject of considerable research, and possesses several points of interest. The independence of the two main constituents (argon being included with the nitrogen) is clearly observable from the table given below; further, owing to the fact that the coefficients of solubility of the individual gases are affected differently with rise of temperature the composition of the dissolved mixture is not constant.
Since oxygen is practically twice as soluble in water as nitrogen, it follows that the dissolved gas is proportionately richer in oxygen. By expelling the gas into a vacuum and reabsorbing it in water, the concentration of the oxygen is still further increased. By repeating these processes several times, a fairly pure oxygen can be obtained, and this has been made the basis of a patent for the commercial separation of oxygen from the air.
The number of cubic centimetres of oxygen and nitrogen (containing argon) dissolved in a litre of water saturated with air from a dry atmosphere at 760 mm. pressure at various temperatures are given in the following table:
Solubility of Air in Water at various temperatures
| Temperature, °C. | 1000β' | |
| Oxygen | Nitrogen | |
| 0 | 10.19 | 18.99 |
| 4 | 9.14 | 17.18 |
| 8 | 8.26 | 15.64 |
| 12 | 7.52 | 14.35 |
| 16 | 6.89 | 13.25 |
| 20 | 6.36 | 12.32 |
| 24 | 5.89 | 11.49 |
| 28 | 5.46 | 10.75 |
Measurement has also been made of the solubility of air in sulphuric acid of varying concentration. At 18° C. the coefficient of solubility in 98 per cent, acid is 0.0173, and in 70 per cent, acid attains a minimum value of 0.0055.
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