the ratio of the specific heats of nitrogen and of...

described above, and it is difficult to see what circumstance led to the conflicting result.

The author is greatly indebted to Prof. Merton for the suggestion of this field of research. The Hilger spectrograph was purchased with a grant from the Royal Society.

The Ratio o f the Specific Heats o f Nitrogen and of Oxygen. 225

The Ratio of the Specific Heats o f Nitrogen and of Oxygen.By J. R. P artington, D.Sc., and A. B. H owe, M.Sc.

(Communicated by Prof. H. B. Dixon, F.R.S. Received December 6, 1923.)

The investigation of the ratio of the specific heats, cp/cv — y, of nitrogen and oxygen described in the following paper was undertaken by a method substantially the same as that used previously with air and carbon dioxide, and described in an earlier communication.*

This consists in measuring the fall in temperature which occurs when a large volume of the gas is allowed to expand adiabatically. If a vessel filled with the gas at a pressure p vslightly greater than atmospheric, is put into communication with the free air, at a pressure by suitable means, so that the equalisation of pressure^ occurs as nearly as possible adiabatically, and if Tj and Ta are the absolute temperatures of the gas before and after expansion, then, for an ideal gas, it is known that

v cpjcv =_________ log Pi - log Pz_(log p x — log p 2) — (log Tx — log T2) ( 1 )

Before considering the details of the method used in the present research reference may be made to the experiments of Mercer, in 1914, and of Shields, in 1917, supplementing the work discussed in the previous communication.

Mercerf used an expansion vessel of only 300 c.c. capacity and attempted to correct for the considerable errors introduced, owing to convection currents from the walls, by making a second determination with a vessel of twice the linear dimensions of the first, assuming that the error introduced was a linear function of this dimension. Twice the difference between the two results was

* J. R. Partington: 4 Physikalische Zeitschrift,’ vol. 14, p. 969 (1913); ‘ Roy. Soc. Proc.,’ A, vol. 100, p. 27 (1921).

t H. N. Mercer : 4 Proc. Phys. Society,’ vol. 26, p. 155 (1914).VOL. CV.— A. Q

on August 20, 2018http://rspa.royalsocietypublishing.org/Downloaded from

http://rspa.royalsocietypublishing.org/

22 G J. R. Partington and A. B. Howe.

therefore added to the first result. This correction for the errors introduced by the use of so small a vessel would seem inadequate. Mercer also omitted to correct for the divergence of the gases employed from the ideal state, on account of the “ great variety of expressions ” which might be used for the correction, and assumed that the latter would in any case be small. The validity of this assumption naturally depends on the degree of accuracy aimed at in the investigation, and in view of the circumstance that Mercer applied corrections for the tarnished condition of the bolometer wire, and other conditions, which raised his experimental value for air from 1 • 382 to 1 • 400, it is clear that a correction for the deviation of the gas from the ideal state, amounting to about 0*001, would not affect his result seriously. It may be noted that Mercer assumed an additive relation for y in correcting his results with nitrous oxide for the air contained in it, and also assumed that the radiation corrections for gases would be in the inverse ratio of the thermal conductivities. In the first case the additive relation really applies to cv, not y, and the radiation corrections in different gases are in the ratio of the squares of the refractive indices, i.e., practically unity.

Shields* used a one litre vessel, and attempted to correct for the errors due to convection and radiation by assuming them to be a function of AT and therefore of Ap. Using different values of Ap, she extrapolated the apparent values of y to zero pressure difference, assuming the relation to be “ practically linear.’ This method of extrapolation has been criticised in the former communication, and appears to be uncertain. Some little uncertainty was also introduced by the use of a galvanometer with an appreciable period, and by the fact that the expansion is stated to be “ oscillatory,” in consequence of which the temperature is measured some definite time after the expansion is complete, which seems undesirable with such a small vessel. Shields used excess pressures of from 7 to 35 mm. of mercury, hardly sufficient to give really accurate results. The results obtained by using different thermo-junctions also differed somewhat widely, especially in the series of determinations for hydrogen at ordinary temperatures, in which case the values of y varied from 1*3781 to 1*4014. When extrapolated to zero fall of temperature, however, the results were in good agreement, which indicates the magnitude of the correction introduced by extrapolation. The final values obtained w ere 1 • 4029 for air and 1*4012 for hydrogen at ordinary temperatures. The latter result in particular seems to -be low, if compared with Lummer and Pringsheim’s

* M. C. Shields : ‘ Physical Review,’ vol. 10, p. 525 (1917).



value of 1 • 4084, which is the only one to which much confidence may be attached.*

In the present research, the expansion vessel, A, fig. 1, consisted of a spherical copper idobe of about 60 litres capacity, provided with two lateral outlets.

The Ratio o f the Specific Heats o f Nitrogen and o f Oxygen. 227

NaOH(2 )

One, about 14 cm. long and 6 cm. diameter, was fitted with a heavy brass screw cap with fibre washer, which could be tightened by means of a pin spanner in order to make it gas-tight. The glass support of the bolometer wires fitted through a hole bored through the centre of this cap and the joint was made gas-tight by means of Faraday’s cement.

The second outlet was of the same length, but 2*5 cm. diameter. This outlet was that through which the expansion occurred and was, in the earlier experiments, closed by a rubber stopper which could be pulled out by means of a cord. The gas was admitted to the globe by means of a narrow copper tube at the top.

The globe was immersed in a water-bath, B, of galvanised iron. The method of supporting the globe in the water-bath was essentially the same as that previously described. Electrical heating by means of a 250 watt radiator lamp immersed in the bath was used, and the temperature controlled by a modified Lowry toluene thermo-regulator with electrical contacts operating a relay. By means of this apparatus the temperature of the bath was kept constant to less than 0 • 01° C., the limit of accuracy of the thermometer employed.

The gases used were contained, initially at a pressure of 120 atmospheres, in cylinders fitted with reducing valves. The particular gas in use was purified in an appropriate manner, and dried by being passed through a wash-bottle of

* Some experiments by the authors, not yet completed, point to a value of y for hydrogen at least as high as that found by Lumraer and Pringsheim.

Q 2



228

concentrated sulphuric acid and through large U-tubes containing, respectively, quicklime, solid caustic soda, and phosphorus pentoxide. The latter was not specially purified.

The principal manometer, C, by means of which the excess of the pressure of gas in the globe over the atmospheric pressure was measured, was a long glass U-tube fixed to a board and filled with colourless paraffin oil of high boiling point, the density of which at t ° C. was found to be 0*8547-0*0005128 t, determined by careful measurements of the density at 17° C. and at 24*8° C., the latter in a thermostat. The weight of oil contained in the bottle was compared with the weight of distilled water it contained at the same temperature. The constants for water were assumed and the expansion of the bottle thus eliminated. The value for the density obtained was confirmed to 0*0001 by an independent determination of the density by the same method by Mr. F. W. Bury, and to 0*0007 by means of a (less accurate) Mohr’s balance.

The levels of oil in the manometer were read to 0*01 cm. by means of a cathetometer with an accurately engraved brass scale. In order that the manometer might not be affected by heat from the water-bath, it was situated in a small room adjoining that in which the remainder of the apparatus was set up. The curtained windows of this room were always kept open whilst an experiment was in progress, and the manometer was screened from the direct rays of the sun. The temperature of the oil was determined by means of two calibrated thermometers attached to the top and bottom of the board supporting the manometer, respectively. In general they agreed to within 0 • 2° C. The mean of the readings of the two thermometers was taken as the temperature of the oil.

The atmospheric pressure, which is taken as the pressure p 2 after expansion, was determined to 0*01 cm. of mercury on a Fortin type barometer, in a room at the same altitude as the laboratory in which the experiments were conducted. The reading was corrected to 0° C., the excess pressure as determined by the manometer being also reduced to millimetres of mercury at that temperature. The initial pressure, p l9 was thus found by adding together this mercury value of the oil column and the corrected reading of the barometer.

The bolometer used to determine the fall in temperature on the expansion of the gas consisted of about 10 cm. of Wollaston wire of 0*01 mm. diameter. The effect of the leads was entirely eliminated by having a second piece, about 4 cm. long, attached to compensating leads, in the arrangement previously described.

The arrangement for supporting the bolometer wires was precisely similar

J. R. Partington and A. B. Howe.



to that previously used except that the part E was omitted (fig. 2 in previous paper). The wires were annealed by passing an electric current of about 2 amperes through them when soldered in position on the support.

The wire used was supplied by Messrs. Johnson, Matthey and Co., Ltd. Wires of 0*001 and 0*002 mm. supplied by this firm, and also by Hartmann and Braun, of Frankfort a/M, were tried, but without success, although such wires from the second source were used in the previous research. Wires of 0*01 mm. diameter were, therefore, employed in all the experiments. I t was found necessary, as will be described later, to apply a correction to the recorded fall of temperature, on account' of the appreciable lag shown by these wires.

The auxiliary mercury thermometer was the same as that previously used. It was carefully calibrated in a vertical position with the normal thermometer No. 58,241 (1914) of the German Reichsanstalt.* No emergent stem correction was necessary, as both thermometers were completely immersed in a thermostat, and in the actual experiments the thermometer was completely immersed in the water of the bath, suspended on a wire. Readings were made through a plate-glass window in the side of the tank.

The four copper leads of the bolometer were carried through a piece of rubber tubing to the resistance apparatus, D, consisting of a Post Office box by Gambrell Bros., London, with an accuracy of 1 in 1,000. The sensitiveness of the bridge was increased by the addition of a supplementary bridge, F, consisting of a piece of eureka wire soldered to copper terminals and fitted with a sliding contact, the whole insulated on blocks of paraffin wax. The slider was connected to the Leclanche cell which provided the current for the bridge, and the two end terminals to the resistance, arm of the bridge, and one of the main leads of the bolometer, respectively. The bridge connections were otherwise as usual, the compensating leads being inserted in the resistance arm. The current passing through the bridge was approximately 2 milliamperes, which was insufficient to cause any appreciable heating of the bolometer wire. The difference between the resistances of the two loops of the latter was about 120 ohms.

The galvanometerA was an Einthoven “ Saitengalvanometer ” made by Edelmann of Munich, with a gold string 0*005 mm. diameter, resistance 130 ohms. The sensibility was 10"8 ampere per scale division, and one-tenth of a scale division could be estimated with the objective and eyepiece used. The

* For the loan of this thermometer we are indebted to the Council of the Chemical Society.

The Ratio of the Specific Heats o f Nitrogen and o f Oxygen. 229



230

field magnets were actuated by a constant current of two amperes taken from the 240-volt power mains, using a suitable resistance and ammeter in series. Connection with the bridge Avas made by means of a reversing key, and a shunt was provided for use in the preliminary adjustments. All the keys were insulated on blocks of ebonite and the galvanometer earthed to prevent interference from stray currents from the magnet system.

In a determination the initial temperature of the bath was raised to about 22° C. and maintained at this temperature by the electric thermostat arrangement. The gas under experiment was forced into the globe to an excess pressure of about 6 cms. of mercury. A preliminary rough adjustment of pressure was made by means of the small mercury manometer (H, fig. 1) and the pressure finally adjusted to its required value. This procedure was adopted in order to avoid continual large disturbances of the oil in the manometer, as it was somewhat viscous and considerable time was necessary for the level to become constant if large changes of level took place. The tube immediately above the levels was always moistened with oil before taking a reading, by a slight displacement of the levels of oil in the manometer.

When the resistance of the bolometer and the reading of the manometer had both become perfectly steady, showdng that the temperature of the gas in the globe had become uniform, the manometer tap, E, was closed and the resistance on the bridge altered to such a value as Avas judged would correspond with that of the bolometer, immediately after the expansion had occurred. The galvanometer and battery keys of the Post Office box were depressed, the galvanometer being, of course, deflected in consequence. The gas was then allowed to expand, in the earlier experiments by pulling out the rubber stopper by means of a cord, and in the later experiments, as will be described, by opening a large stopcock. The galvanometer deflection then fell practically instantaneously to a position near the zero of the scale. This position was noted and the whole operation repeated, using the same excess pressure and initial temperature, but Avith a slight alteration of the sliding contact of the supplementary bridge, as indicated by the deflection obtained in the previous expansion. This was found more convenient than the method previously adopted, of altering the pressure.

When, after two or three trials, the deflection returned precisely to zero after expansion, the temperature of the bath, the levels of the manometer, the temperature of the latter, and the height of the barometer Avere carefully read. Sufficient Avater was then baled out of the bath to permit of the addition of ice, which Avas added until the galvanometer, with the bridge unaltered, was




again steadily at zero, with all the ice melted. The water was kept in motion by means of the stirrer and the final adjustment of temperature was accomplished by adding a little more ice or by turning on the heating lamp for a few seconds. On account of the large mass of water in the bath this final temperature adjustment could be performed with accuracy. The temperature of the bath was then carefully read on the mercury thermometer and the measurement was completed.

A few determinations were first made with air in order to check the values obtained with the apparatus against those obtained in the former research. After a few preliminary experiments, the values obtained for y for air were 1-3928 and 1-3968, there being some uncertainty to within 0-05° in the measurement of the final temperature in the second determination.

These results being somewhat low, a correction was applied for the fact that the wires used in the bolometer might have an appreciable effect on the result on account of their larger heat capacity. Some experiments referred to in the earlier communication showed that the deflections obtained corresponding with the same fall of temperature with wires of different diameters were approximately in linear relation to the diameters.* In the case of wires of 0-001 and 0-01 mm. diameter respectively, the deflections were in the ratio 377/372, although the lag in the case of 0-01 mm. wires was insufficient to cause any visible sluggishness in the deflection of the galvanometer.

Whilst it seems desirable to make further experiments relative to the effect of the thickness of the wire used for the bolometer, this has so far been impossible owing to failure to obtain a good specimen of the thin wire, but experiments are still proceeding. Meanwhile, although the authors feel confident that the data quoted above are sensibly correct, it is necessary to regard the results involving this correction as being of a somewhat provisional nature, possibly requiring slight modification at some future date.

In fig. 2, representing the bridge, let R and S be the resistances of the ratio arms,P the resistance of the bolometer wire, and Q the balancing resistance in the box. Let the potential difference across the bridge be e and the resistance of the galvano-

* ‘ Roy. Soc. Proc.,’ A, vol. 100, p. 31 (1921).

The Ratio o f the Specif c Heats o f Nitrogen and o f Oxygen. 231

e

F i g . 2.



232 J. Ii. Partington and A. B. Howe.

meter. G. Then it has been shown by Adcock and Wells* that for the case where compensating leads are inserted in Q, where R — S, and where a “ parallel ” arrangement of the thermometer and compensating circuits is adopted :

P - Q(2)V = e

1 + i ) ( P + Q ) + R 4 - \G1 PQ

where V is the potential difference across the galvanometer. Then if C is the current flowing through the galvanometer :—

C =_______________ P - Q _____________ _

P G + R + 2Q -f- )-j- QG -J- RG -f~ QR(3)

In this expression, C and P, in the case under consideration, are the only variables.

Thus : M l _ Cj K - C 2a p 2 c 2 k - c / (4)

where• /

G + R + 2Q Q R , G

In the case under consideration GJCj = 372/377, and Cx and C2 are of the order of 10~8 X 15 = 1-5 X 10-7 amp. K is of the order of

1 -4/(100 + 1000 + 250 + 1000) = 6 x lO"4 amp.The factor (K — C2)/(K — Cx) is therefore very nearly unity and we

have:APi= Cia p 2 c 2’ (5)

that is, if, after balancing the bridge, a variation occurs in the resistance of the bolometer wire, the current then flowing through the galvanometer will be proportional to the change of resistance of the wire, and therefore to the change in temperature. For small deflections, the deflection is proportional to the current flowing through the galvanometer,t and therefore the true final temperature of the gas will be given by the relation,

T , = T1 « ( T 1 - T a#) # l i (6)where Tx is the initial temperature, T2 the final temperature, and T2' the apparent final temperature.

The two foregoing determinations were now recalculated, using the above

* 4 Philosophical Magazine,5 vol. 45, p. 541 (1923). t Crehore : * Philosophical Magazine,5 vol. 28, p. 210 (1914).



correction. The calculation of all the following determinations was made in the way described in the previous paper (p. 42).

The two preliminary experiments with air gave y = 1* *4004 and y —1*4038. These results were considered in sufficiently close agreement with those previously obtained for air to form a test of the apparatus, and it was decided to proceed with the determination of the ratio of the specific heats of nitrogen.

The Ratio o f the Specific Heats o f Nitrogen and of Oxygen. 233

Experiments with Nitrogen. •

The nitrogen was supplied in cylinders by the British Oxygen Company. They stated its composition to be : nitrogen, 99 • 6 per cent. ; oxygen, 0 • 2 per cent. ; neon, 0*045 per cent. ; helium, 0*15 per cent., by volume.

The oxygen was removed by passing the gas, after being taken from the cylinder by means of a reducing valve, through a heated hard glass tube containing copper turnings. A correction for the neon and helium present was applied to the final result. The gas was then dried, as already described, by tubes containing quicklime, caustic soda, and phosphorus pentoxide.

The following results were obtained for nitrogen :—

P i

mm. 805- 6 801*3 803*5 829*5 832*84 831*63 826*33 817*12 812*65 810*60

Results with Nitrogen. Series I.

V 2* Tx- Ts.

mm. O O744*7 295*10 288*52740*3 295*04 288*44741*6 295*16 288*49768*4 295*22 288*79772*17 295*30 288*97771*52 295*30 289*03765*54 295*19 288*78756*72 295*23 288*82752*43 295*25 288*84752*20 295*24 288*76

y ' (uncorrected).

1*40201*39971*3990*1*4045*1*40151*40071*40301*39991*3987*1*4028

Mean y ' = 1*4012 ±0*0006f

* Rejected later. | Including results marked *.

After the completion of the results for oxygen, a second series was obtained for nitrogen, in order to obtain a result with a smaller mean error than the abo\e, and in order to determine whether the results obtained for nitrogen were too high owing to “ overshooting ” of the expansion, as the first results obtained with oxygen were found to be.*

* See later, p. 239.



234 J. R. Partington and A. B. Howe.

The following results were obtained :—Results with Nitrogen. Series II.

P i - P% - T x. T 2. y ' (uncorrected).

m m . m m . O o803-81 745-17 296-27 289-93 1-4000815-86 757-22 296-26 289-99 1-4022831-98 772-10 296-26 289-97 1-4025830-96 772-00 296-26 290-08 1-4011833-54 775-35 296-27 290-18 1-4025

From these results it was evident that 44 overshooting ” had not previously taken place in the case of the nitrogen. The mean of both series was therefore taken.

Rejecting now the third, fourth and ninth results of the first series, as diverging too greatly from the mean value, we obtain from the two series a mean value of / = 1-4015 ± 0-0003.

This result now requires correction for the effects of radiation and for the divergence of nitrogen from the ideal state.

In order to correct for radiation, we have to increase the value of y by 0-0021, as has been shown in the earlier communication. Applying this correction, therefore, we obtain :—

y for nitrogen at 20° C. = 1-4015 -j- 0-0021 = 1-4036 ± 0-0003.The value of y = cplcv was also shown to be given by the equation

y = / [1 + ( / — 1) l i ttt3] = y ' < f > , (7) a relation deduced from the characteristic equation of D. Berthelot, where

71 — (Pi + Pz)I^Pc, and T = 2TC/(T1 + T2), (8)pc and Tc being the critical constants. In the case of nitrogen, 33-0 atm., Tc = 126-5° abs. The value of <f> at 1-03 atm. pressure and 20° C. is therefore 1 • 00086. From this we find :

y — cplcv for nitrogen at 20° = 1-4048 ± 0-0003.This result still requires correction for the small quantities of helium and

neon in the nitrogen.Whilst for a mixture of gases the ratio of the specific heats cannot be regarded

as the mean of the values for the constituent gases, the specific heat at constant volume may be so regarded in correction terms. In order, therefore, to correct for the presence of the helium and neon we must first calculate the specific heat of the sample of nitrogen at constant volume.



The specific heats at constant volume and at constant pressure may be calculated from the ratio cPjcv = y, when the difference, cp — cv, or, more conveniently, M (cp — cv) = Cp — C„ where M is the molecular weight, is known. This may be obtained from Berthelot’s equation :—

Cp — C, = 1*985 (1 + y-jv 7TT3) — 1*985 </>' gram cal., (9)

where n and t have the values given by (8).*In the case of nitrogen at 20°, <p' = 1*0043, hence Cp — C, = 1*9935 (15°)

grm. cals., whence C, — 1*9960/0*4048= 4*9247, for the actual gas. Now the percentage composition by volume of a mixture of gases is also the percentage molecular composition. Moreover we may take the molecular specific heat at constant volume for both helium and neon to be 3*0 with sufficient accuracy, and the nitrogen contains 0*195 per cent, by volume of inert gas. Therefore the value of C, for pure nitrogen will be

(4*9247 — 3*0 X 0*00195)/0*99805 = 4*9286.

Thus Cp = 4*9286 + 1*9935 = 6*9221. From these figures for pure nitrogen at 20° C. and 1 atm. pressure :

Y = ty C , = 1 • 4045 ± 0 • 0003.

The values of the specific heats per 1 gram of nitrogen will be

cp — 6*9221/28*02 = 0*2470 grm. cal., and cv = 4*9286/28*02 = 0*1759 grm. cals.

The work done by former investigators on the specific heats of nitrogen is as follows. Masson,f in 1858, calculated the ratio of the specific heats from the velocity of sound in the gas, obtained by sounding an organ pipe in an atmosphere of nitrogen. He obtained a value of 1*415 for y, which is unreliable. Masson obtained identical results for all the permanent diatomic gases.

RegnaultJ found a value of 0*2375 for the mean cp for air between 15° and 200 C., and 0*2175 as the mean of two determinations for oxygen, between 15 and 200°. Taking air to be 80 per cent, nitrogen and 20 per cent, oxygen by volume, he obtained the value of 0*2438 for cp for nitrogen by calculation.I his calculation was, however, made on the assumption, which cannot now be held to be correct, that cp can be regarded as an additive quantity for a

* The value of R taken is 1*985 gram cal. (15°) per 1°.t M. A. Masson : ‘ Annales de Chimie et de Physique,’ vol. 53, p. 265 (1858).t V. Regnault: ‘ Mem. Acad. Sci.,’ vol. 26, pp. 110, 303 (1862).




236

mixture of gases. It is not therefore possible to compare Regnault’s value with that calculated from the results of the present research.

Cazin,* in 1862, determined the ratio of the specific heats directly, using the method of Clement and Desormes, and a somewhat improved apparatus. He obtained a value of y = 1*41 ± 0*02. This result requires correcting for radiation and deviation from the gas laws, but the correction is not within the limits of error of the experiments.

Holborn and Austin,! in 1905, determined the mean cv for nitrogen over various ranges of temperature, by a calorimetric method. From their results we may calculate the true cv at 20°, and obtain a value of 0*2319 grm. cals.

In 1907, Holborn and Henning,! by a calorimetric method, determined the specific heat at constant pressure of nitrogen for the ranges, 1400° — 110° C., and 800° — 110° C. By extrapolation from these values they obtained the following expression for the mean specific heat between 0° and t° C.

= 0*2350 + 0*0000191.Whence cp (true) at 20° = 0 • 2358 grm. cal.

Pier, in 1909,§ obtained a value for the mean molecular heat at constant volume of nitrogen by mixing it in known proportions with electrolytic gas in a bomb, and finding the maximum pressure produced on explosion. From a series of results he obtained the expression for nitrogen :

mean C, = 4 • 900 + 0 • 00045 t.If the validity of the extrapolation is assumed, this gives, at 20°, C, (true) =

4*918 grm. cal.Scheel and Heuse,|| in 1913, determined cp for nitrogen by a constant flow

calorimetric method. They obtained the following results at 20° : cp = 0*2492 ; whence Cp = 6 • 983 ; C„ = 4 • 989 and y = 1 • 400. The second and third values were obtained by calculation from CP using Berthelot’s equation, and the following values for the critical constants of nitrogen : Tc = 124° abs. ; and pc — 27*5 ats. Recalculating using the more recent values Tc = 126*5° and jpc = 33*0 ats., we obtain Cv = 4*990 and y = 1*399. It may be noted that the value found for cp differs by about 5 per cent, from Holborn and Henning’s value.

* A. Cazin : ‘ Annales de Chimie et de Physique,’ vol. 66, p. 206 (1862).t Holborn and Austin: 4 Wiss. Abhand. der Phys.-Tech. Reichsanstalt,’ vol. 4, p. 133

(1905).t Holborn and Henning: ‘ Annalen der Physik,’ vol. 23, p. 809 (1907).§ P ier: ‘ Zeitschrift fur Elektrochemie,’ vol. 15, p. 536 (1909).II K. Scheel and W. Heuse : 4 Annalen der Pliysik,’ vol. 40, p. 473 (1913); ‘ Zeitschrift

fur Elektrochemie,’ vol. 19, p. 593 (1913).




Schweikert,* in 1915, determined the velocity of sound in nitrogen at 20° C., by a modification of Kundt’s method. He calculated 337-7 metres per second at. 0° C., from which he calculated y =1-4061. This requires correction and gives y —1 -402.

Dixon, Campbell and Parkerf have determined the velocities of sound in nitrogen at temperatures from 0° to 1000° C. by actual measurements in a long coiled tube contained in a furnace. Their values are corrected for the difference of the velocity in a tube and in the free gas, and the ratio of the specific heats calculated from the corrected velocity by means of Berthelot’s equation. At 0° they found 337-5 metres per second to be the velocity of sound in the free gas, and at 100°, 394 • 1 metres per second. In the calculation of the values of the specific heats from this velocity we obtain at 0°, Cp/Cv = 1-406 and C„ = 4-914, whilst at 100°, Cp/C„ = 1-402 and C„ = 4-948. Interpolation from these values gives at 20° C. : Gp/Gv 1-405 and C„ = 4-921 in excellent agreement with the result of the present research.

Schulze and Kathjen,| by another modification of Kundt’s method, and correcting by van der Waals’s equation, obtained as a mean of twelve experiments a value of 1-4144 ± 0-0002 for G for nitrogen at room temperature and atmospheric pressure. They used a value for air of 1-4044 in order to calculate the value for nitrogen. If we use the value for air, 1-4034, obtained in the previous research, and Berthelot’s equation, we obtain for nitrogen a value of 1-412, which seems to be too high.

These results may now be tabulated with the results of the present research for purposes of comparison. Calculated values are enclosed in brackets.

The Ratio of the Specific Heats o f Nitrogen and o f Oxygen. 237

Results with Nitrogen.

Observer. 7- c/* Cv. Temp.

Masson............................. 1-415°C.

Gazin ............... 1-41 ± 0 -0 2 _Hulbom and Austin ............... 0-2319 20Hoi bom and Henning ........... 0-2358 _ 20Pier .............. 4*918 20Scheel and Heuse (1*399)

(1*402)(1*405)1*4120

0•2492 (4*990) 20Schweikert ..... 0Dixon, etc. .......... (4*921) 20Schulze and Rathjen —Present Research 1*4045 (0-2470) (4*929) 20

* G. Schweikert: ‘ Annalen der Physik,’ vol. 48, p. 59.3 (1915). t Dixon, Campbell and Parker : ‘ Roy. Soc. Proc.,’ A, vol. 100, p. 1 (1921).+ P. A. Schulze and H. Rathjen : ‘ Annalen der Physik,’ vol. 49, p. 451 (1916).



238

Our results are seen to be in excellent agreement with those of Dixon, Campbell and Parker, which appear to be more accurate than any of the other previous measurements described. This we regard as an important confirmation of the accuracy of our method.

Experiments with Oxygen.

The oxygen used was “ electrolytic oxygen,” compressed in cylinders and supplied by the British Oxygen Company. It contained as impurity only about 0*2 per cent, of hydrogen, which was removed by passing the gas, on its way to the drying tubes, through a hard glass tube containing heated platinised asbestos. The gas was dried by being bubbled through concentrated sulphuric acid and passed through tubes containing quicklime, solid caustic soda, and phosphorus pentoxide, as already described in the case of the nitrogen.

A series of fifteen results were first obtained for oxygen. The agreement was not so good as was desired, the values for y', uncorrected for radiation and divergence from the gas laws, varying from 1*3892 to 1*4014.* These irregularities were not observed in the case of nitrogen. In addition to the erratic values obtained, difficulty was experienced in making the trial expansions for each determination, the deflections obtained in successive expansions, after slightly varying the position of the bridge slider, not being quite consistent. In order to eliminate this effect, it was decided to try a brass stopcock through which to make the expansion.

The aperture of the stopcock was rectangular, and about equal in area to a circular tube of 1 centimetre diameter. The expansion now took from ^ to 1 second to complete. The irregularities were then found to be eliminated completely, but the galvanometer deflection was about half a small scale division less than before, this difference corresponding to about 0 • 10° less fall in temperature.

With a view to determining which deflection could be regarded as correct the following experiments were carried out. An expansion was made using the stopcock, and a perfectly steady deflection obtained. The bridge was balanced so that immediately after expansion the deflection was zero. Another expansion was then made under exactly the same conditions, except that the usual full opening and rubber bung were used instead of the stopcock. (Diameter of outlet tube = 2*5 cms.) The deflection now obtained was not

* It may be desirable to point out that the degree of reproducibility here attained is more satisfactory than that of previous experimenters, but it is not regarded as sufficient for the accuracy aimed at in the present research.

J. 11. Partington and A. B. Howe.



perfectly steady, but the immediate value was approximately half a small scale division larger than that obtained with the stopcock, thus confirming the result previously obtained. A tube of 1 • 1 cm. diameter was now tried, with a rubber stopper. The deflection was perfectly steady, and of the same magnitude as that obtained using the stopcock. Finally, a tube of intermediate diameter (1‘6 cm.) was used. The deflection was intermediate between those already obtained, but was not steady, and was not consistent for two successive expansions. I t was therefore decided to use the stopcock for future work, as it was evident from the foregoing experiments that slight irregularities had been introduced owing to the gas “ overshooting ” in the expansion through too large an aperture. The occasional use of a still smaller aperture, caused by the stopcock not opening fully, did not modify the deflection obtained, although the expansion was in that case considerably slower.

The numerical results obtained in the experiments with oxygen just described were as follows :—

Initial temperature in each case = 23 • 16° C.Using stopcock.—Final temperature = 16-99°. — 1-3919.Using rubber stopper and f i d l opening (2-5 cm.).—Final temperature =

16-88°. y ' = 1-4019. 'As was previously mentioned, this overshooting was not observed in the

case of nitrogen. I t thus did not seem probable that the results so obtained would have to be discarded. Their validity was demonstrated by the second series of results when the stopcock was used, which gave a mean value for the ratio of the specific heats almost identical with that from the first series.

A series of results for oxygen was now obtained.


Results with Oxygen.

Pi- P2• T ,. T a. y ' (uncorrected).

mm. mm. O O826-19 766-43 296-23 290-04 1-3912819-34 759-58 296-25 290-00 1-3919810-40 750-45 296-25 289-92 1-3909809-22 749-88 296-31 290-04 1-3905819-88 760-05 296-32 290-07 1-3916818-59 758•63 296-29 290-03 1-3902817-63 758-63 296-21 290-04 1-3920823-15 763-31 296-21 290-00 1-3904821-69 762-14 296-34 290-16 1-3921820•17 762-05 296-33 290•28 1-3903

Mean y ' = 1,3911 ±0-0002



240

In order to check still further the previous decision that the higher results obtained with the rubber stopper and large aperture were in reality due to overshooting during expansion, a determination was now made with oxygen, using about half the former excess pressure. Under these conditions it might be expected that the overshooting would not be so likely to occur, and the same result would probably be found whether the stopcock or the rubber stopper was used. It was found that the deflection when the rubber stopper was used, though not quite so steady, was, within the possible accuracy of the measurement, identical with that using the stopcock. This determination gave the following figures : p ± = 787*17 mm. ; p 2 = 756*87 mm. ; Tx = 296*25° ; T2 = 293*02° ; giving y = 1*3873 ; a result of the same order as the results obtained at the higher pressure using the stopcock, and thus confirming the assumption regarding overshooting.

The above mean result requires correction for radiation and for divergence of oxygen from the ideal state, as in the case of the nitrogen. For oxygen, pc=. 50*2 atm., Tc = 154*25° abs. Thus at 20° C. and 1*04 atm. pressure, <p — 1-0010. The radiation correction is 0*0021, and therefore

y = cvjcv for oxygen at 20° and 1 atm. pressure.= (1*3911 + 0*0021) 1*0010 ± 0*0001.= 1*3946 ± 0*0002.

Calculating the specific heats at constant volume and at constant pressure, as in the case of the nitrogen, we have :—

<f> = 1*0051, hence Cp — Cr = 1*9951 grm. cals.Thus Cv = 1*9951/0*3946 = 5*0559 grm. cals.

Cv = 5*0559 + 1*9951 = 7*0510 grm. cals.For 1 gram of oxygen these become

cv = 0 • 1581 grm. cals, and cv = 0 • 2294 grm. cals.These results may now be compared with those obtained by other workers.Masson obtained the same value, 1*415, for y for oxygen and for nitrogen.

Dulong,* in 1829, also determined the ratio of the specific heats for oxygen by a method similar to that of Masson, and obtained as a mean result, y = 1*415. Kegnault, as already indicated, obtained calorimetrically for cv the value 0*2175 for oxygen, the mean of two determinations. If we increase this by 1/160 of its value, as considered necessary by Leducf in the case of air, on account of Regnault’s neglect to take account of the expansion of the gas in

* Dulong: ‘ Annales de Chimie et de Physique,’ vol. 41, p. 113 (1829).1 Leduc : ‘ Comptes Rendus,’ vol. 126, p. 1860 (1898).

J. B. Partington and A. B. Howe.



The Ratio of the Specific Heats o f Nitrogen and o f Oxygen, 241

passing from the heater to the calorimeter, we obtain 0-2188 cals. Cazin obtained 1-41 ± 0-02 for y for oxygen.

An accurate direct determination of cP/cv for oxygen was made by Lummer and Pringsheim* in 1894. They obtained the value, y = 1-3977, corrected for radiation and deviations from the gas laws. They used, however, commercial oxygen (“ kauflicher Sauerstoff ” ), containing probably about 9 per cent, of nitrogen by volume. Lummer and Pringsheim’s results have been recalculated using the method of correction by Berthelot’s equation employed in the present research. The results were practically identical with those using f C -f- 1/a, where a is the coefficient of expansion of the gas, instead of the absolute temperature, the method adopted by Lummer and Pringsheim. If we correct their value for the presence of the nitrogen, using the method employed in the present paper in the case of the determinations for nitrogen, we obtain 1-3970, using the value of Cv for nitrogen calculated from the results obtained in the present research. Correction for small quantities of the inert gases present in the “ commercial oxygen ” would, of course, further reduce this result.

Holborn and Austin, in 1905, obtained a series of results for cp (mean) for oxygen, by the method employed for nitrogen, from which we calculate

(true) at 20° to be 0*2195 grm. cals. Scheel and Heuse, in 1913, determined cv for oxygen, by the calorimetric method, and obtained the following results at 20°: cp — 0-2182 grm. cals.; whence Cp — 6-982 grm. cals. ; C„ =-= 4-989 grm. cals., and y == 1-399.

Schweikert, in 1915,by modification of Kundt’s method, obtained 315-7 m.p.s. as the velocity of sound in oxygen at 0°, from which he calculates y — 1 -4049. Correction gives 1-402 by Berthelot’s equation by multiplying by

Tabulating the results in order to compare the results of the present research with those obtained by other workers we have :—*

Results with Oxygen.

Observer. 7- 0„. Temp.

Masson..... 1*4151*415

° C.DulongRegnault.......... 0*2188 15-200Cazin ...... 1*41 ±0*02

1*3970 ±0*0004 (1*399)

Lummer and Pringsheim Scheel & Heuse Holborn and Austin 0*2182

0*2195(4*989) 20

20oSchweikert ....... 1 *402

1 *3916 ±0*0002Present research. (0*2204) (5*056) 20

* miner and E. Pringsheim : ‘ Annalen der Physik,5 vol. 64, p. 555 (1898).VOL. CV.— A. k



242 J. R Partington and A. B. Howe.

A portion of the absorption of heat represented by cv in the case of an imperfect gas is used in performing intermolecular work due to attractions existing between the gas molecules. The correction to the ideal state can be made from the following formula, derived from Berthelot’s equation :—

C*° (ideal) = C„ — # | B. ttt3 (10)Cp° (ideal) — C*° + 1-985 grm. cals. (U)

Vo (ideal) = Cv°jCv°. (12)

The values of (27/32) X B -tt3 at 20° are : for nitrogen, 0-0042 ; for oxygen. 0 • 0050. Thence.:—

cv . cp . Cv C,. a ° . 7* To-

Nitrogen at 20° C. Oxygen at 20° C.

0•1759 0 1581

0-24700-2204

4- 9295- 056

6- 9227- 051

4- 9255- 051

6- 9107- 036

1 - 4045 1-3946

1-4030 l -3930

A check on the above figures is the calculation of the values for air from the determined values for nitrogen and oxygen tabulated above.

Assuming that C.„ for air is composed additively of the values of C„ for theconstituent gases, and that air has the following composition by volume ..Na= 78-1 per cent., 0 2 = 21-0 per cent., A — 0-9 per cent., and that C* for argon is 3-0, we find :—

C„ (calculated for air) = 4-929 X 0-781 + 3-0 X 0-009 + 5-056 X 0-21 = 4 • 939 grm. cals.

Leduc* uses substantially this method in order to calculate the value of the. ratio of the specific heats for a mixture of gases from the known values for the constituent gases.

As is not absolutely independent of pressure, the value of ( for oxygen at 1/5 atmosphere pressure, and that for nitrogen at 4/5 atmosphere should be used in the above calculation. These values may be calculated from the relation,

C„, — C#1 == R -r3 (7T2 — 71+ (13)

derived from Berthelot’s equation. The correction is, however, so small as to be within the limits of experimental error.

Before comparing the result calculated above with that obtained for air directly, it is necessary to refer to an arithmetical error in the previous com

* Leduc : ‘ Comptes Hendus,’ vol. 160, p. 338.



munication.* The paragraph on p. 46, dealing with the calculation of the specific heats at constant volume and constant pressure, should read as follows:—

“ In the case of air at 17°, <j>' = 1-0042, hence Cp — Cy = 1-993 grm. cal. The values for 1 grm. of air are : cp — cv = 1-993/28-99 = 0-06875 grm. cal., cv= 0-06875/0*4034 = 0-1704 grm. cal., cp = 0-1704 + 0-0687 — 0-2391 grra. cal.”

The molecular heats corresponding to these values are therefore Cp = 4-947 and Cp = 6-933 grm. cals.

It will thus be seen that the values of Cv for air from the value of y observed directly, and that calculated from the values of y determined for nitrogen and oxygen, are in excellent agreement.

It is also necessary to refer to a second arithmetical error in the previous paper. In calculating the “ ideal ” values for air and carbon dioxide the values of (27/32) X R tut3 at 17° are : for air, 0-0042 ; for carbon dioxide, 0-0264. We can thus correct the table on p. 49 as follows :—


Cv C p . Cv. C!,. Cy°. c / . 7* 7o-

Air at 17° C........... 0 1704 0-2391 4-940 6-933 4-936 6-921 1-4034 1-4021Carbon dioxide at

17° C............. ...... 0 1531 0-1996 6-744 8-782 6-718 8-703 1-3022 1-2955

Finally the authors desire to thank the Government Grant Committee of the Royal Society for a grant which has largely defrayed the expenses of the investigation.

* ‘ Proc. Roy. Soc.,’ A, vol. 100 ( 1921).

VOL. CV.— a s



the ratio of the specific heats of nitrogen and of...

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