W2 = N (I + Pp + Qp2)

Transcription

1 Physics. - Measurements about the velocity of sound in hydrogen gas at liquid hydrogen temperatures. By A. VAN TTERBE EK and W. H. KEESOM. (Communication N0. 216c from the Physical Laboratory at Leiden). (Communicated at the meeting of September ) 1. ntroduction. n Comm. N0. 213b 1) we put for the square of the velocity W of sound in helium gas aquadratic formula W2 = N ( + Pp + Qp2) where prepresents the pressure. From the coefficient N we can calculate the ratio (cp/c.)p=o (see 5. Comm. N0. 213b). This ratio. which is free from the mutual interactions of the molecules. may show how the rotational energy for the case of more-atomie molecules dies out at decreasing temperature. From thermodynamical reasoning it follows that the coehicient P is equal to wh ere R is the gas constant = j B is the second virial coefficient. and À equals M(c.)p=o! RM. The determination of th is coefficient P is the more important as measurements on the dependency of the velocity of sound in a gas on pressure can be made at pressures lower than one atmosphere. hence at the boiling point and even at still lower temperatures. wh ere direct measurements of B by means of the compressibility are difficuit. As for hydrogen gas there exists a series of determinations 2) of va lues of B. determined with the classica 1 method of measuring isotherms. we have tried to verify those values. We have also established a formula for the values of B as function of the temperature by using our measurements together with the known values of the second virial coefficient. Such a ) These Proceedings : ) J. PALACOS and H. KAMERLNGH ONNES. Archiv. Néerl. sér. A Comm. Leiden No H. KAMERLNGH ONNES and F. M. PENNNG. Arch. Néerl. sér. A Comm. Leiden No. 165b. F. P. G. A. J. VAN AGT and H. KAMERLNGH ONNES. These Proceedings Comm. Leiden No. 176b.

2 989 formula enables us to calculate (Cp Cv ) and Cv from the velocity of sound. We intend to publish t'he results of these calculations before long. 2. Experimental method. We followed the method described in Comm. N b 1). From researches made by GRÜNESEN and MERKEL 2) and besides from those made by CORNSH and EASTMAN 3) it follows that it is possible to reduce, by using a wide resonator, the correction due to the wal!. which is inversely proportional to the diameter. The same is true for the correction due to the end-openings, the more even so as this correction is inversely proportional to the second power of the diameter at least. The correction due to the end-openings cau also be eliminated by using a very long tube or by employing ton es of high frequencies. The authors mentioned above used both these methods. But at hydrogen temperatures these methods present experimental difficulties. One of these results from a very important damping of sound when passing through the narrow connecting tubes (see Fig., Comm. N0. 213b). For this reason we have used a very wide resonator, diameter 6.2 cm. The length of the resonator is mm at 0 C. Before soldering the covers on the tube this was polished carefully. The correction due to the wall was made just as in Comm. Nos. 209a 4), 209c 5), 213b. Before beginning the measurements at hydrogen temperatures we determined the velocity of sound in carbon-dioxide-free air at 0 C. We found m/sec., whereas in Comm. N0. 213b we found m/sec. 3. Measurements with hydrogen gas at hydrogen temperatures. The hydrogen gas used for the measurements was obtained hy evaporation of iquid hydrogen. As during each series of measurements the hydrogen gas was kept for three hours at hydrogen temperatures we estimated it not to be superfluous to check the percentages of ortho- and para-hydrogen at the beginning and at the end of the series of experiments. Mr. A. BJL, assistant at the Leiden Cryogenic Laboratory, was so kind as to make for us this test by the heat conductivity method. He did not observe a change of the percentages. Table gives the results of the measurements. W ob. mean5 the observed va lues of the velocity of sound in the hydrogen gas coufined in the resonator, W tlle velocity for t he free gas, obtained by correcting for the wall effect. ') loc. cito 2) E. GRONESEN and E. MERKEL. Ann. d. Phys. 66, 341, ) R. E. CORNSH and E. D. EASTMAN. Journ. Am. Chem. Soc i) These Proceedings : 33, HO ) Wls- en Natuurkundig Tijdschrift

3 TABLE Velocity_ of sou ï d in hydrogen gas. -~- -~-=1 TemperatuTe Date of the Pressure W ob. 1 W avetage ok measurement at mls <c March 26, '31 May 8, '31 MaTch 26, '31 June S, '31 MaTch 26, '31 June S, '31 May mls,c, -~------~ ~ Tune 22, ' i L May 8. '3 1 May 8. '31 May 8. '31 March 30. '31 May 8. '31 Ma Tch 30. '31 June 22. '3 1 --'---- -, r !:~ : ~ ' 340.~ '------

4 991 We have drawn, in Fig., Was function of pat each temperature EC 338.0~----~-~,----~----~------~----~ o - P A T. Fig. 1. L-l March 26, 8 March 30, V May 8, 0 June 15, A June 22, ' Calculations. We calculated from the measurements given in Table the following data : 1. (Cp cv)p == o. For th is purpose we adjusted the quadratic formula, mentioned in, to the determined va lues of W2 by calculating the coefficients N, Pand Q with the method of least squares. Making use of N=RMT(S!) M Cv p== o we calculated (cp cv)p =o, The molecular weight M of the hydragen gas we put The results of these calculations we gi've in Table 11. The small deviations from (cpl cv)p==o = are probably due to the uncertainty originating from the extrapolation to p = o.. _ 2 db 2 2d2B 2. CalculatlOn of 5 - B + :3 T dt+ 15 T dt2' Fram the results of Table 11 it follows that at the temperatures of liquid

5 992 ~mperatur:--! OK TA BLE ~~~ :::: :~ hydrogen }., = t (see ). 50 th at S depends on B as mentioned above. We calculated the value S == t RT. P from the coefficient P of the quadratic formula mentioned in. For this purpose we followed a method somewhat different from t-hat we followed in the calculations mentioned under 1. We now aclded to the values W, following from the observations. the point Wo = R7vt T (~p),where (~) = v p=o v p=o thus considering W o as an observed point, and applied then the method (lf least squares. The values of N, P, Q, and S calculated in this 'Way we give in Table 111. TABLE Temperature N P Q (mlsec. )2 OK at- at- 2 S 1 1_7~ ' We rem ark that the sign of the coefficient Q changes between K and K. This depends on the curve W 2 = f(p) becoming convex towards the p -axis. whereas it was concave towards thp. same axis at higher temperatures.

6 993 The values S of Table 111 are drawn graphically as a function of temperature in Fig X1O SDr-----~~---r r_--~ S 1 '.0 1ho6;-_- ----=T,...,,~7---,f.:B:----,.,.,9;:------=20::; ==210K. Fig. 2. o From the velocity of sound. A. V Calculated from known values of B. We observe that the value of S at presents an important deviation from the curve. This deviation may be owing to the small number of measured points (see Table ) at this temperature. 3. For the purpose of verifying the known va lues of B we used the following method. Through the points T = B = ); ; ; ; derived from measurements of isotherms by PALACOS. KAMERLNGH ONNES and VAN AGT 2). we laid the quadratic formula 103. B = _ ;3 _ 2~128. This function gives us the va lues of S. drawn in fig. 2. curve. We may expect that the values of S obtained in this manner are strongly dependent upon the function of Band hence also strongly dependent upon the choice of the points by means of w'hich the function B is fixed. We have calculated a second series of va lues of S from the formula B = r- - T2- la1d through the values of B at the three highest of the above-mentioned temperatures. These last values of S have been drawn also in fig. 2 (curve 11). We see that the experimental va lues of S lie between the curves land 11 ) Average of values of B at and ok (VAN AGT and KAMERLNGH ONNES). and at 20,"19 ok (PALAClOS and KAMERLNGH ONNES). 2) loc. eit.

7 994 obtained from known values of B. From this fact we can conclude that the agreement of the values.of 5 calculated from known values of B, and those obtained from our measurements. is rather good. 5. Calculation ot B as a tunction ot T trom compressibility measurements together with measurements ot the velocity ot sound. To calculate this function we first tried aquadratic formula in 11T. But we found that it was necessary to put 103. B = a + f + ;2 + ;3 to get a good agreement with the measured values of Band the measured values of S. The coefficients of this last formula have been calculated by the method of least squares from a system of 11 equations. 6 of them resulted from the values of B mentioned under to which a suitable weight was given (see column 4 of Table V). The oï'her 5 equations resulted from the va lues of 5, given in Table 111. From these calculations followed 1) : 103. B = _ 53~ ~; i-l~ _ 5.16; ~ 10 4 (1) Fol' comparison. we give Table V. in which B- and S-calculated mean : derived from formula (1). T OK TABLE V. - -~~--~~ Measured Weight Calculated ) ) B h S ) As this formula depends on measurements in the temperature range from 20.s o K down to 11.SoK. it can be trusted for this temperature reg ion only; extrapolation s only al!owed over a rather smal! range. 2) Average of values of B at 20,53 and ok (VAN AGT and KAMERLNGH ONNES). 3) Average of three values B. viz. at ,19 and ok (PALAClOS and KAMERLNGH ONNES).

8 995 n Table V we give a set of values of B deduced from formula (1). 1-- o~ O.3~ We thankfully acknowledge that this research was furthered by a grant from the SMTHSONAN NSTTUTON. We also thank Mr. J. A. VAN LAMMEREN, phil. nat. cand., for his helpful assistance with the measurements and calculations.. Summary. n this communication we relate about measurements of the dependency on pressure of the velocity W of sound in hydrogen gas at hydrogen temperatures. The results are given in Table. From these measurements we calculate (cp/c.)p=o by an extrapolation to p=o (see Table 11). We found that it is possible to represent the dependency on pressure by means of the formula W2=N (1 + Pp + Qp2). The coefficients of this formula are represented in Table 111. From known values of the second virial coefficient B together with va lues of S, derived from the coefficients P of the quadratic formula mentioned, we calculated B as a series according to powers of 1 ft including the third one. A set of values of B calculated from this formula are given in Table V. ERRATA. W. H. KEESOM and A. V. TTERBEEK. Proc. XXXV p. 207: Table 11 5th column: omit 104 p. 208: Table V 5th column : omit 104. p. 208 fig. 2: for 160 X 10 6 read 160 X 10 2 Proceedings Royal Acad. Amsterdam. Vol. XXXV