1918 W2.4- WARNER ThE PRESSURE (NCR EASE IN THE CORONA. Digitized by the Internet Archive in 2013 http://archive.org/details/pressureincreaseOOwarn UNIVERSITY OF ILLINOIS THE GRADUATE SCHOOL F e ftrnaryLJa 191 8 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPER- VISION BY _ EA^L.&.~^ap.AC2...-"uJLg^^E ENTITLED THE PBffP'TJ * I\CRKft:?S I U.I., X ~L A.. - BE ACCEPTED AS FULFILLING THIS PART OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHTT.ORDPWY TW PHVfiTHR Head of Department Recommendation concurred in :* Committee on Final Examination* ^Required for doctor's degree but not for master's. THE PRESSURE INCREASE IN THE CORONA BY EARLE HORACE WARNER A. M. University of Illinois, 1914 A. B. University of Denver, 1912 THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN PHYSICS IN THE GRADUATE SCHOOL OF THE UNIVERSITY OF ILLINOIS 1918 PRESS OF THE NEW ERA PRINTING COMPANY LANCASTER, PA. I ( Reprinted from the Physical Review, N.S., Vol. VIII., No. 3, September, 1916: and Vol. X., No. 5, November. 1917.) THE PRESSURE INCREASE IN THE CORONA. By Earle H. Warner. L Introduction. THE "corona" is the glow which surrounds conductors when there exist high potential differences between them and neighboring bodies. A careful study of the corona phenomena is necessary (1) to determine the factors which regulate the loss of power due to the corona, which on long transmission lines may be an important item, and (2) to obtain data from which a theory can be developed which will, with mathematical rigor, explain the corona effects. The first of these objects has been quite successfully carried out by Peek, Whitehead, Ryan and others. The only advances toward a theoretical explanation of the corona have been made by Bergen Davis 1 and Townsend. 2 In these two theories the authors have assumed that the corona is an ionization phenomenon. That is, they assume that the high potential difference causes the few ions which are always present in a gas to move with a velocity sufficiently great to break the molecules with which they collide into two parts, one bearing a positive charge and one a negative charge. All these charged particles then move, because of the influence of the field, toward one or the other of the terminals. The presence of these ions thus explains the conductivity of the gas and the acceleration of the ions explains the light effect. If the corona is an ionization phenomenon one would expect, if the corona apparatus was inclosed, at the instant the corona appeared, i. e., at the instant the molecules were broken up into ions, that the pressure in the apparatus would increase; because according to kinetic theory the greater the number of particles in a given volume the greater the pressure. This pressure increase was first discovered by Dr. S. P. Farwell, 3 working in this laboratory and has been discussed 3 "The Corona Produced by Continuous Potentials," Proc. A. I. E. E., November. 1014 later by J. Kunz. 4 The above mentioned theories assume ionization but do not account for such a pressure increase. Under certain circum- 1 "Theory of the Corona," Proc. A. I. E. E., January. 191 1. 2 "The Discharge of Electricity from Cylinders and Points," Phil. Mag.. May, 1914. 4 Dr. Jakob Kunz, "On the Initial Condition of the Corona Discharge," Phys. Rev. July, 1916. 3 Ukii . in 4 EARLE H. WARNER, stances this pressure increase can amount to as much as three cm. of mercury. Arnold 1 has contended that the pressure increase could be completely accounted for as the result of Joule's heat, and that the assumption that it is due to ionization is untenable. To support this contention Arnold performed experiments " by electrically heating the central wire in apparatus similar to Harwell's and " observed the pressure increase. With such an apparatus Arnold attempted to show (i) that an increase in pressure due to heat appears suddenly, (2) that for a given power consumed in the tube the increase in pressure due to heat is of about " the same magnitude as those observed " in the corona. In order to show clearly that the pressure increase is not due to heat a series of comparative experiments were performed with the pressure increase caused, first, by producing the corona glow on the wire and, second, by heating the central wire. The pressure increase observed in the first set of experiments will be referred to as caused by corona and in the second set as caused by heat. A few computations have also been made which strengthen the results of the experiments. Since the conception of ionization is so intimately associated with the idea of increase in pressure, it seemed important to determine the laws, relating this ionization pressure to the corona current. II. Theory. Dr. J. Kunz has developed a theory which predicts how this pressure increase should vary with the current. One can best understand his development by thinking of the corona as occurring around a wire which is coaxial with a cylinder. See Fig. 1, which represents a cross section U C -V Fig. 1. • Fig. 2. of such a corona tube. Suppose the ends of the tube to be closed, so as to inclose a constant volume u c . When the wire is connected to a very high positive potential and the case grounded the corona glow- appears around the wire and the pressure instantly increases from at- 1 H. D. Arnold, (Abstract) Phvs. Rev., Jan., 1917. I _J V THE PRESSURE INCREASE IN THE CORONA. 5 mospheric to some higher value. Let the condition of the gas at the beginning of the experiment be represented by the point A, on the p — v plane. (See Fig. 2.) The volume is then v and the pressure p . Step I. — Apply a potential difference e between the wire and the case. Some current i will flow and the pressure will immediately jump from p to a higher value, say pi. The state of the gas will now be represented by the point C. The work done by the current per second, ei, will then be equal to the increase of internal energy of the gas A U, plus the work done by the gas W u due to the pressure increase. This energy equation gives us ei = AU + Wl (i) Step II. — Let us force into the tube a small amount of gas. This will require work dW 2 and the pressure will increase from pi to pi + dpi and can be represented by the state point B. Then dW-, = — Vodpi. (2) The total work to change the gas from state A to state B has then been ei + dW- z = AU + \\\ - v«dpi- (3) Now let us start again with the same initial conditions and by two different steps arrive at the same final condition. Step III. — When the state of the gas is A let us force in a small amount of gas. This will require work dW 3 and the pressure will increase from po to p + dpo, which may be represented by the state point D. Then dW z = - vodp . (4) In the existing conditions the size of the current depends not only on the potential difference but also upon the initial and final pressures. The increase in current causes an increase in pressure which tends to stop the current. The steady condition of the current represents a condition of equilibrium between the attempt of the current to increase the pressure and the attempt of the increased pressure to stop the current. Step IV. Now apply the same potential difference e. Let that current i' flow so that it will cause the pressure to increase from po + dp* to pi + dpi, that is, so that the state of the gas can be represented by B. Then as in Step I. ei' = AU' + W t . (5) In the last two steps the total work required to change the state of the gas from A to B is ei' + dW s = AU' + W 4 - vdp . (6) Then by the law of the conservation of energy, the work required to *nioq 9ffj ycf u e'wig nobcnp) havr vtiwQSn Urn h\>/f Ihj>iJ nil •j jjnijfsiy.s jrlf ul n ni -wmni >rlT .1M9V1IJ > )ffl IjOlH liliupo \o noililxro-) l \ d-' W( -f i«S[ 0» .I f. jjr: ni rwtiT ■jrft 6 EARLE H. WARNER. change a system from one state to another is independent of the path, we have At/ + W x - vodp! = At/' + W, - vudpo or At/ - At/' + Wx - Wi = v (dp, - dp ). Subtracting t5) from (i) we have At/ - At/' + W\ - W A = e(i - V). Therefore But Then and integrating e(i — i') - Vo(dp! — dp ). i = V + di. edi = v d(pi — po) Vq ki = — (pi — po) + a constant. (7) (8) (9) (10) (II) (12) Since (pi — po) represents the increase in pressure, that is, the ioniza- tion pressure, this equation shows that the ionization pressure should be exactly proportional to the corona current. It was the object of the experiments which have been performed to test this relationship with pure gases in the tube. III. Apparatus. The constant potentials were obtained from a battery of continuous current shunt-wound 500-volt generators connected in series. The corona tube was of the wire and coaxial cylinder type. (See Fig. Fig. 3. ■una aw ^i) moil (?J ^nhomtduS THE PRESSURE INCREASE IN THE CORONA. 7 3.) Glass plates with holes for the wire to pass through were sealed to the ends of the tube so that the holes were on the axis of the cylinder. The wire, No. 32, copper, passed through the holes and was thus coin- cident with the axis of the cylinder. The wire was sealed into these holes and held taut by red sealing wax. To the cylinder was soldered a small 1! T" tube, one side of which was joined to the vacuum pump and the other side Was connected to a Bristol aneroid pressure gauge. The increase in pressure was measured by this Bristol gauge. Any increase in pressure caused it to bend slightly and so rotate the mirror. By observing the deflection of a beam of light over a scale, which had previously been calibrated by reading simultaneously the deflected beam and a water manometer connected directly to the gauge, the increase in pressure in cm. of water could be determined. The advantage of such a pressure measuring instrument in this experiment is that it is very quick Maotun» Tenoinaio. u w Kolvln V»Ur» , .«r. Y"ltch. Pole — Cl PGbongur Ga\v*nomo Braaa Fig. 4. in its action. The instant the pressure increases the gauge jumps right- up to its new position and a reading can be taken in a very few seconds. It was necessary to read this pressure increase quickly because if much time was required, the heating effect of the current would increase the pressure also. The current was measured by a Type H D'Arsonval galvanometer. The apparatus was connected as is shown in Fig. 4. EARLE H. WARNER. . 1 .50 .1.25 30 40 50 Time in Seconds. Fig. 5. IV. Experimental Results. 1 . The reason why one who sees this pressure increase, as recorded by a quick-acting pressure meter, thinks it is not a heat effect, is because of rapidity with which it appears and disappears. Arnold showed that the pressure increase occurred quite rapidly when caused by heat. The following curves show the difference in the rapidity of appearance and disappearance of the pressure increase caused by heat, and caused by corona. It will be noticed in Fig. 5, where the pressure increase was caused by heating the central wire, that fifteen seconds was required for the pressure to come to its maximum value, and that from the time the current was broken twenty-five seconds was required for the pressure to return to practically its original value, while in Fig. 6, where the pressure increase was caused by co- rona, only three seconds was required for the maximum pressure to be at- tained and that the pressure came back to practically its original value in eigh- teen seconds. In this last case from the appearance of the phenomenon it seems, if the aneroid pressure me- ter had less inertia, that the pressure increase could be determined in less than three seconds. These curves show that the pressure increase appears five times as rapidly when caused by corona as when caused by heat, and disap- pears also more rapidly. 2. In the pressure increase due to corona, a short time interval of five to seven seconds occurs after the sudden increase of pressure, before the heat effect in the corona begins to be noticed. This is shown by an abrupt bend, A, in the curve where the pressure in- crease is plotted against time, as is done in Fig. 7. No such bend occurs in the case where the pressure increase is caused by heat alone, as is shown in Fig. 5. In the work which has previously been reported the pressure increase measurements were always taken at the point A , and this seems to be practically independent of the heat effect. 3. The heat which is produced in the corona discharge, shown by the gradual pressure increase from B to C, Fig. 7, is distributed throughout the whole volume of enclosed air and so, when the current is broken does not Preesure Incr«aeo Due To Corona . C 1-25 0.75 Time in See . Fig. 6; H fetGOq n't amh i!'jbf"»wa if THE PRESSURE INCREASE IN THE CORONA, radiate rapidly because the air is a poor conductor. This is shown very clearly in Fig. 8. This seems to show that the pressure increase due to heat in the corona is represented by the difference of ordinates of C and B (Fig. 8). As soon as the corona current is broken at C the? increase in pressure due to corona at once disappears, but the increase in pressure Pressure Increase Due To Corona. 10 20 JO 4o 50 60 70 to 90 Time In Seconds. 20 40 60 CO 100 120 140 160 1*0 200 Time in Seconds. Fig. 7. Fig. 8. due to heat in the corona discharge remains, as is shown by the difference of ordinates of D and A. This difference is always very nearly equal to the difference of ordinates of C and B. This heat energy produced by the corona current, since it is distributed through the gas, radiates very slowly, as is shown by the gradual descent of the curve from D to E. No such effect is observed when the increase of pressure is due entirely to heat, as is shown in Fig. 5. This curve (Fig. 5) shows that twenty-five seconds after the current through the wire is broken at C the resultant pressure increase due to heat has practically disappeared; while Fig. 8 shows that twenty-five seconds after the corona is removed from the wire the increase in pressure due to the corona has disappeared, but practically all the pressure increase due to heat in the corona (ordinates C minus B approximately equals ordinates D minus A) still remains and radiates very slowly. 4. If the increase in pressure is due to heat, the same increase in pressure should result when the same power is consumed ( *« Fig. 16. is one of the exceptional cases where nitrogen is largely ionized at lo\ temperatures and thus probably chemically active. X S i 14 EARLE H. WARNER. How nitrogen, carbon dioxide and ammonia are ionized, are questions which require further study. The arrangement of the apparatus could be used as a high potential voltmeter by simply calibrating the increase in pressure against volts, as determined by a disc electrometer. 6 : 3 3 a c £ 2. e * u < Relation Between I0HI2ATI0B PRESSURE and CORONA CURRENT Tire +. T3 2. Currant la 10'* Aaperot. Fig. 17. V. Results from Theoretical Considerations. 1. If the increase in pressure is due to heat it is possible to compute the magnitude of the pressure increase when one knows the watts of electrical energy consumed in the tube. The trial represented in Fig. io gives us this data. The observed pressure increase was measured in three seconds so that the total number of joules of work consumed by the tube in that time was 3 X 0.266 = 0.798 joules and this corresponds to 6.1909 calories. Knowing the volume of the tube, the temperature and pressure of the air in it, the mass of the air in the tube can be com- puted. With the above-mentioned quantity of heat and mass of air, together with the specific heat of the air at constant volume, the temper- ature rise of the air can be computed, assuming that the electrical energy is converted into heat. This temperature rise comes out to be 2. 44° C, which at constant volume corresponds to a pressure increase of about nine cm. of water, while the observed pressure increase in this particular trial amounts to about seven tenths cm. of water. In this computation radiation and conduction losses have been neglected because they would be very small from a body 2.44 C. above room temperature. This shows that the observed results lie in a different order of magnitude from what would be expected if Arnold's theory were true. 2. Arnold states, if " we compute the corona currents that would result from the presence of enough ionized particles to produce the ob- .flRWIKYI .Yl CUflKTV - THE PRESSURE INCREASE IN THE CORONA. 1600 served pressure changes, the currents calculated are many thousand times greater than those actually obtained." Such a statement is only true when the ionized particles are produced in a uniform or practically uni- form electric field. This is not the case in the corona tube. H. T. Booth is publishing data on the distortion of the field in the corona tube. This data shows that the potential gradient near the wire is very high — of the order of 30,000 volts per cm. This is the arcing gradient, in which it is probable every molecule is ionized. Then for a long space between the wire and the tube there is a very small gradient. With this condition of the field, near the wire every molecule may be ionized and still the resultant current be very small, for few of the ionized particles near the wire will pass through the space where there is a small gradient. Simple computations based on kinetic theory show that the maximum observed pressure increases can be explained by ionization if every molecule of the air with- in 1.39 mm. of the wire is ionized. Within this distance the potential gradient is equal to the arcing gradient and therefore probable that all mole- cules are ionized. VI. Further Verification of Kunz's Theory. The final equation as pre- sented above is Do ki = — (pi — po) + a constant, where i is the corona current, v the volume of the tube, e the potential difference between the wire and the tube, p x — p the pressure increase, k a con- stant and p the initial pressure. This equation shows that for a con- stant potential difference e, the current i should increase as p is low- ered. Data was taken, by measuring the current at various measured pressures, caused by a constant potential difference, which verifies this theory. This data is shown graphically in Figs. 18 and 19 when pure hydrogen and nitrogen respectively were the gases in the tube. 400 540 440 J40~ Pressure In of Maroury. Fig. 18. 16 EARLE H. WARNER. VII. Summary and Conclusions. Experimental results show: 1. That the increase in pressure due to corona appears and disappears much more rapidly than when due simply to heat. 2. That the heat in the corona discharge is not a prominent factor until many seconds after the corona appears. 3. That in equal energy experiments the increase in pressure due to corona differs from the increase in pressure due to heat[by about 50 per cent. 4. That at the instant the corona appears the gas injthe tube at a small distance from the wire is cooled. TB " 720 680 640 600 560 520 PresuuTO In Hro. of lioroury. Fig. 19. 5. The ionization pressure in the positive corona is exactly proportional to the corona current in dry air, hydrogen, nitrogen, carbon dioxide, oxygen and ammonia. 6. Any chemical action that takes place due to the corona is exactly proportional to the corona current. 7. That the theory advanced by Kunz is verified in one more field, namely in the relation between current and pressure for constant voltage. These results together with conclusions drawn from simple calculations, force one to believe that the pressure increase in the corona discharge is | r~ Vi Yj — jr ■ ■ ■ P I I 0001 \ •Pi .3m THE PRESSURE INCREASE IN THE CORONA. *7 not due to Joule's heat. With the recent knowledge of the distortion of the field in the corona tube it seems very possible that the increase in pressure is due to ionization. The writer desires to express his appreciation to Professor A. P. Carman for the use of the laboratory facilities, and to Dr. Jakob Kunz for his continued interest and suggestions. Laboratory of Physics, University of Illinois, June. 1917. .fiQi .sauL VITA. Earle Horace Warner completed his secondary training at the Manual Training High School of Denver, Colorado. In 1908 he entered the L diversity of Denver and from it, in 1912, received his A.B. degree. Since 1912 he has been a graduate student at the University of Illinois. In 1914 he received the degree of A.M. from the University of Illinois. He has held the following positions: Assistant in Physics, University of Denver, 1910-1912; Assistant in Physics, University of Illinois, 1912-1917; Instructor in Physics, University of Illinois, 191 7 1918. He has published the following papers: "Determination of the Laws Relating Ionization Pressure to the Current in the Corona of Constant Potentials," Physical Review, N.S., Vol. VIII., No. 3, p. 285, 1916: "The Pressure Increase in the Corona," Physical Review, N.S., Vol. 10, No. 5, p. 483, 1917.