Thermal Conductivity Bridge for Gas Analysis CLARKE C. MINTER AND LYLE M . J. BTJRDY :Vaval Research Laboratory, Washington 25, D . C. “convection” can be combined with “conduction” to produce a bridge which can be made specific for either hydrogen or carbon dioxide. Because the method can be used in the analysis of any ternary mixture of gases in which the thermal conductivities of the constituents are sufficiently different, it can doubtless be applied to many industrially important mixtures of gases as well as to numerous analytical problems in the laboratory.
The need for a simple and accurate analytical method of indicating the concentration of hydrogen in a ternary mixture containing carbon dioxide led to the development of a new thermal conductivity bridge for gas analysis. It is now possible to analyze a ternary mixture, such as hydrogen and carbon dioxide in air, without having to remove one constituent by absorption. The conventional thermal conductivity bridge is modified in such a manner that
T
HE: thermal conductivity bridge has been used for years in the analysis of a number of frequently occurring gas mixtures. The apparatus has been of rather conventional design and has consisted of current-heated filaments suitably mounted i r i sniall cells, some cont,aining the mixture to be analyzed and othcrs containing a standard comparison gas, usually air. Be(‘ause the filaments are connected in the form of a Wheatstone l)ridge, any difference between the rates of heat loss from the filamr.nts in the two gases \ d l cause the bridge to become un1)alaiired to an extent. depending on the composition of the inisture. BRIDGE NO I
BRIDGE
niques are described by means of \+hich it is now possible to indicate the concentration of either hydrogen or carbon dioxide i n an air mixture containing both gases without having to remove the carbon dioxide by absorption. h E W PROCEDURE
The new method employs two thermal conductivity bridges, as shown schematically in Figure 1. Bridge 1, in which the cells have a diameter of 3 / 1 6 inch, is conventional, xhile biidge 2 is of unconventional design, having cells xvith a diameter of 3//4 inch. ;ill the filaments used in the two bridges ( I and 2) are as nearly as possible exactly alike, but the difference i n cell diameter has an appreciable effect on the heat loss from the filament when both types of cells contain air, so that when both bridges carry the same current bridge 2 with the large cells will have the higher resistance. I n addition, the difference between the rate of loss of heat in the large cell and that in the small cell becomes greater as the thermal conductivity of the gas decreases In other words, the new method makes use of what has previously been regarded a8 gaseous “convection” in thernial conductivity cells, the effect of which is known to increase not only with the molecular weight of the gas but also as the diameter of the cell is increased The possibility of using convection together with conduction as a physical method of gas analysis was pointed out by Minter ( 1 ) in a paper describing the relation between pressure and the convection effect in thermal conductivity cells of a given diameter. By means of this relation it n a s possible to determine the composition of a ternary mixture of gases. I n the present method the pressure remains constant and the convection effect is produced by increasing the diameter of the cells, as in bridge 2 . Because bridge 1 with the small cells gives practically a pure conductivity effect, while bridge 2 adds a certain amount of convection t o the conduction, a given mixture of hydrogen or carbon dioxide in air would be expected to produce different results in the two bridges in Figure 1. The effect of adding hydrogen to a gas such as air is to reduce the convection effect, so that the increase in total heat loss caused by the addition of hydrogen is not so great in the large cell as in the small cell, and the output potential difference from bridge 2 is less than from bridge 1. On the other hand, when carbon dioxide is added to air the convection effect is increased and the decrease in heat loss is less in the large cell than in the small cell, and again the output from bridge 1 is greater than from bridge 2 .
NO 2
Figure 1. Circuit for Testing Gas Mixtures in Dissimilar Bridges
‘The two binary mixtures most frequently analyzed by the thrimal conductivity method are: (1) small concentrations of hydrogen (0 to 5%) in air, and (2) carbon dioxide (0 t o 20%) 111 air. The conductivities of the two mixtures varv with the concentrations of hydrogen or carbon dioxide-increasing with hydrogen, whose conductivity is greater than that of air, and decreasing with carbon dioxide, whose conductivity is less than that of air. Because of this variation, the gas compositions can be measured easily by a meter with calibrated scale connected across a thermal conductivity bridge It frequently happens, however, that an unknown mixture contains air, hydrogen, and carbon dioxide. In such cases it has been impossible to indicate the concentration of either hydrogen or carbon dioxide by comparison with air in the simple bridge described. It is necessary then to employ the “differential” method, which consists in measuring the difference in thermal conductivity of the mixture before and after the absorption of carbon dioxide, as well as the difference between the carbon dioxide-free sample and air, due account being taken of the increase in concentration caused by the removal of carbon dioxide. The inconvenience of having to remove the carbon dioxide from the mixture is a disadvantage which has retarded the use of thwmal conductivity. I n this paper new apparatus and tech-
EXPERIMENTAL
The filaments used in the two bridges are all alike, being a single piece of 0.0015-inch Kovar wire 8 mm. long, spot-welded on two supporting wires. The cells of each bridge in which the 143
ANALYTICAL CHEMISTRY
144
-
filainrnts are mounted arc drilled ill a brass block with suitable diffusion holes for admission of air and the sample gas. The two bridges of Figure 1, one with small cells and one with large cells, are connected in series with a G-volt storage battery, a rheostat, and a milliammeter. The output terminals of thr two bridges are connected t o a potentiometer or to a millivoltmetcr. The gas mixturm were dried before passing through thc ttvo blocks, in both of which dry air was the comparison gas. Only three mixtures were employed-air and 5Y0 hydrogen; air and 5% carbon dioxide; and air, 5% carbon dioxidc, and 5% Iiydrogen. It, is safe t o assume that in these small coiicentratio,ns the outputs from the air-hydrogen mixture and from thc aircarbon dioxide mixture arc linear up t,o 5% and also that, tho effect of adding carbon dioxide t o any air-hydrogen mixturc is lincar up to 5% carbon dioxide. Assuming the linear effect, the output data for the t.wo bridges (1 and 2) produced by the three niixtures are used t o construct, liricar graphs from which can be ol)tained equations connecting the outputs ( E 1and E ? )of the two bridges with the hydrogen and the carbon dioxide concentrations. Or, conversely, the unknoLvn percentages of hydrogen and carbon dioxide can br calculatcd from the outputs El and E?.
INDICATOR
CENTER OFF
SERIES RESISTAKES
Ld,L/A
C M C U I N G 41R
BALAYCE
+3 0
+25
/
4 BRlDOE
+20
+ I5
BRIDGE NO 2
NO I
Figure 3.
Indicator Circuit for Two Bridges
cxprcssions used to calculate the percentages of hydrogen and carbon dioxide from the potentials shown in Figure 2 and Table I can be derived by starting with the relation which states that the output from a bridge is proportional to the product of the hydrogm sensitivity (potential difference produced by adding 1% hydrogen to air) and the sum of the per cent hydrogen and the per cent carbon dioxide times a factor.
+IO
+5
W
E
O
W
k 1
-
P5
5 PERCENT
Let HZ = % TI? coz = %COP SI = Hz sensitivity in bridge 1 SI = Hz sensitivity in bridge 2 E , = output from bridge 1 E, = output from bridge 2 .4nd we have for the two bridges
Up IN MIXTURE
E1 = SI(&
Figure 2. Open Circuit Potential Difference Obtained from Two Bridges
The experimental data obtained are given in Table I and plotted in Figure 2. It can be seen that the potential output produced by a given air-hydrogen mixture relative to air is greater from a small-cell bridge than from a large-cell bridge, and that t,he output potential produced by a given air-carbon dioxide mixture is likewise greater from a small-cell bridge than from a large-cell bridge. As a further illustration of the difference in the characteristics of the two bridges, it \vas found that when the mixture was air and 5% carbon dioxide tho sinall-cell bridge gave an output of -3.85-mv. open circuit, while the output from the large-cell bridge was only -1.35 mv. I n bridge 1 the effect of the carbon dioxide was balanced by the addition of 0.ilYo hydrogen t o the mixture, while in bridge 2 it was balanced by the addition of only 0.370 hydrogen. Because the cffect of adding carbon dioxide t o an air-hydrogen mixture is to reduce the output potential of the bridge, it is clear that the difference between the effects in the t \ T o bridges can be employed very uniquely to dctcrmine both hydrogen and carbon dioxid? in the mixturc. EMPIRICAL RELATIONS
The method can be explained by expressing the per cent hydrogen and the per cent carbon dioxide in a given mixture as functions of the difference in output from the two bridges. The
+ FiCOz) + FzCOz)
Ez = SI(HB
(1)
(2)
F , and Fz are negative factors which express the reciprocal of the per cent carbon dioxide necessary t o balance the effect of 1% hydrogen.
Experimental Data
Tahlc 1.
Composition of Mixture
Output Potential (Open Circuit), Mv.--_ Bridge 1 Bridge 2 (small cells) (large cells) -3.85 -1.35 27.00 24.50 23,l5 23.15
Solving Equations 1 and 2 for H2 vie have
(El/Sl) - FICOZ
(3)
112 = (E*/S1)- FZC02
(4)
IT,
=
and Equating Equations 3 and 4 and solving for COS we find
CO,
=
(ExlSi)- (Ez/Sz) FI - Fz (5)
V O L U M E 2 3 , NO. 1, J A N U A R Y 1 9 5 1
145
.\Is0 from l.:tiuatioii,q 1 a i i d 2 ~vcxhavr~
:iii c.Icctrica1 indication of the diff.,rcJnce between the tivo products in Equat,ion 0 can hc m:idc t o rxpress directly the per w r i t rarbon dioxide in the mixture, no niatter what the hydrogen eentt’iit of the mixturc. In practice i t would not be ncccss:iry actually t o obtain t h e p d u e t s as shown in Equations !I and 10. The same result is ol)t:iined if we do nothing a t all t o E2 but reduce E1 to the extent c~illedfor in the cquatioris. What is required is an instrument 2.115 for indicating the differrim bctn-cen Ez and - El. This dif2.333 fi.rrrice would be directly proportionnl to per cent carbon dioxide rrg:irdlcss of the hydrogen content. Likewise an instrument 0 117 \vhich would indicate the difference between Ea and -fl1 0.333 could tie made to indicate thc pcr cent hydrogen regardlcss of thc carbon dioxide content. .in indicator circuit for this method is shown in Figure 3.
illlll
The movement of the indicator is composed of two exactly siiiiilar coils on the same shaft. Any movement of the coil is due to the difference in the potential difference applied t o the terminals of the coils-which depends on the magnitude of E, and E2 and the values of the various series resistances thrown into the indicator circuit hy means of the two-pole, two-throw sn-itch with center-off position. I n each pair of leads to bridgcs 1 and 2 there is placed a shorting switch, so that the air balancc of cnch bridge map be checkcci separately and adjusted if nccessarv COMBISATION T A E R \ l A L CONDUCTIVITY BRIDGE
Figure
4. Circuit Diagram Combination Bridge
of
Equations 5 and 8 permit the unknown percentages of carbon dioxide and hydrogen in the mixture, air-carbon dioxide-hgdrogen, to be calculated simply by measuring the potential difference outputs, E1 and E2, from the two bridges. The values of the constants ( K l , K2, &, and K : ) are easily calculated from the experimental data by measuring E , and E2 for mixtures of known compositions. Employing the data given in Table I, the numerical values of the constants in Equations 5 and 8 can be readily calculated, and we find that the equations become
- 2.115Ei
(9)
0.333E2 - 0.117Ei
(10)
CO? = 2.3332 and
I&
Equations 9 and 10 can now be employed to calculate the percentages of hydrogen and carbon dioxide in mixtures of these two gases in air up t o 5% of each, simply by reading the outputs from the two bridges and making the substitutions for E1 and E2. Although this procedure could be employed without much difficulty in the laboratory, it would be desirable to have a direct iiidicat,ion of the percentages of carbon dioxide and hydrogen in an unknown mixture of these gases in air. It has been found possible t o obtain a direct, indication of the unknown percentagcs: the method and apparatus are described below. The solution of the problem is t o be found in Equations 9 and 10. Equation 10, for example, states that if the output, E2, from bridge 2 is multiplied by 0.333 and the output, El, from bridge 1 is multiplied by 0.117, then the percentage of hydrogen in the mixture is given by the difference between the two products regardless of the carbon dioxide content of the mixture. It is a very simple matter t o obtain an electrical indication of the difference between the two products just mentioned, and the indication could be expressed in terms of the per cent hydrogen in the mixture, as stated in Equation 10. I n the same manner
While the technique of using t ivo bridges and the circuit of Figure 3 is preferable under certain conditions, the next logical step in the developnicnt of thc nrw principles and the new app:irat,us would be to c.niploy only one bridge for the analysis. Such a bridge has bccn made and tested and the predictions of its performance have been cornplet.ely verified by experiment. The new bridge circuit, shown schematically in Figure 4, contains half the small-cell bridgp, half the large-cell bridge, and two exactly similur incrt ohmic resistors. One large cell and one small cell contain air, and t,he mist,ure t o be analyzed is contained in the other conibination of cells on thc opposite side of the bridge. B r ~ a u s conly half of hridge 1 anti half of bridge 2 are in the n c hridge, ~ thc output, potential diffcrcnce tvith the annulling resistors shorted out will be equal t o half the difference b r t w x n thc outputs from the two bridges in Figurc 1. The operation of the new bridge is explained below. Suppose that with the annulling resistors out of the circuit one set of cells in Figure 4 cont,ains air while the other Pet eontains a mixture of carbon dioxide in air. It is observed t.hat, there is a potential diffrrence across the bridge. If now the annulling resistors are placed in the bridge as shown and gradually increased in resistance, keeping both exactly equal a t all times, with the current through the bridge the same, the potential difference across the bridge will gradually decrease, owing t o the action of the inert resistors in reducing the difference betvccn the drops across t,hosc arms of the bridge containing the sinal1 cells. When the annulling rcsistors have attained a certain value i t is observcd that thcre is no potential across the bridge, which has noiy beeomc, insensitive t o carhon dioxidc. The bridge will now indicate the presence of hydrogen, rcg:irrlless of n-hether o r not thp mixture contains carbon dioxide. Thc effect of the two annulling resistors in Figurc 4 in conditioning the bridge t o be sclccti\-c or specific for one of the ronstituents of a mixture of t h r w g:i~cscan be undcrstood from Figure 2. When conditioning for hydrogen, for example, the output from the small cells for a c:trl)on dioxide-air mixture is rcduccd by the resistors until it eyu:ils the output from the large rcllsthat is, the output from thc small cells is reduced from -3.85/2 to -1.35/2, so that thc half of the bridge containing the small cells produccs the same potential difference as the half containing the large cells, and the bridge is balanced. S o w when hydrogcn is addcd t o the misturc, thr output from the small cclls with
146
ANALYTICAL CHEMISTRY
the annulling resistors in the circuit is less than the output from The results obtained with some hydrogen-carbon dioxideair mixtures are given in Table I1 and plotted in Figure 7. the large cells and the difference between the two is proportional to the per cent hydrogen regardless of the carbon dioxide content. I t can be seen from Table I1 and Figure 7 that the effect of The filaments of the combination carbon dioxide has been reduced to negligible bridge are mounted in cells of suitproportions by means of the annulling resistors, able diameter drilled into a brass and that the results show a high degree of block as shown in Figures 5 and 6. linearity, which was to be expected from other Because the combination bridges considerations. Other tests have shown that the used in the first tests yielded an output rather too low for practical opera: tion, a new high resistance element YAR RET/STANCL E.! EM€NTS was developed. The new element L A R G r CELL consisted of 4 inches of 0.0025-inch D/AM Kovar wire wound in the form of a helix and completely embedded in a thin layer of glass to give it permanent Figure 5. Top View of Bridge s
