Use of Convection Effects in Gas Analysis by Thermal Conductivity CLARKE C. >[INTER, Gow-Muc Instrument Company, 'Yezcark, 4.J .
A method has been developed for analyzing a terilar) mixture of gases b? comparing its thermal conductivity with that of a binary mixture of k n o w n composition and then comparing the effect of pressure on con>ection for the two mixtures. While the ternary mixtures in\estigated consisted 0nl3 of h?drogen, carbon dioxide, and methane, the method should be applicable to other rombinations of gases that do not react chemically with each other.
4PPARATTrS &\I) METHOD
G"'
analysis by means of thermal conductivity has hecn found useful in many laboratory and industrial problems, one advantage is that the thermal conductivity of a gas is independent of density and is therefore not affrcted by changes in prcsssure. In most, commercial types of thermal conductivity equipment, however, the deflection on an indicator produced hy a gas having a given conductivity is not wholly independent of the pressure of the gas being analyzed. U-hen this ocrurs, it can be interpreted as indicating that convection, as \tell as conduction, is playing a part in the process, since natural convection in gases varies with the pressure, while true conduction is not affected (2). The ideal thermal conductivity apparatus should be so designed that variations in pressure produce no rhanges in deflection on an indicator, and some commercial equipment is fairly good in this respect. Khile convection should be avoided, it is posFible to make use of convection effects in a novel manner by designing an apparatus in which the Convection effect is accentuated. Since the magnitude of the effects of pressui'e on convrction depends uniquely on the nature of the gas, it is possible to analyze a ternary mixture of gasea by comparing its thermal conductivity with that of a binary mixture of known composition and then comparing the effect of pressure 011 c.onvc>ctionfor the two mixtures. The loss of heat by natural Convection can probably 13c espressed by a relation such as ir
The apparatus employed is shown schemstically in Figure 1 and photographically in Figure 2. The apparatus consists of a nheatstone bridge circuitland a null-point indicator (millivoltmeter). The cells in the brass block are so designed that the filaments lose an appreciable amount of heat by convection. Each cell is connected to a calibrated glass buret, equipped with a stopcock for admitting and removing gases, and a mercury leveling bulb for changing the volume and the pressure. A voltmeter and rheostat are provided to enable a constant voltage to be applied across the bridge. The sensitivity of the null-point indicator isl adjusted by nieans of a variable shunt (not shown). The ternary mixtures inveitigated methane, and carbon dio.ridr.
contained hydrogen.
WH EATSTO N C
ALVANDMLfER
B R A S S BLOCK
in which H is the heat lois, I' is the absolute p r e k w e , and S ia a convection factor depending on the nature of the gas. Just how convection varies x i t h ptessure is not of much interest here (I), but the variation of convection with the nature and thc concentration of the gas is of importance in this discussion. The effect of pressure on convection is so negligiblj- small for hydrogen that there can be no heat transfer by convection, and X in the equation above is zero for hydrogen. For all other gases X has a positive value which in general increases n i t h the molecular weight of the gas. The relation between convection and other physical properties of a gas does not appear to have been investigated. A tentative approximate relation between conductivity and convection in a gas might be written as
0
LEVELING BULB W I T H MERCURY
RUBBER TUBE
That is, the convection factor, X , in a gas is proportional to the logarithm of the ratio of the absolute conductivities of hydrogen and the gas in question. This problem is very interesting theo~rtically,and will be discussed in another paper.
Figure 1.
464
Schematic Diagram of .Apparatus
JULY
1947
465
+
loticring the pressure of the binary mixture (H3 CHd, which can be called ( AP),. The ratio of t.hcse two pressures is then an inverse measure of t.he ratio of t,he convection factors for the two mixtums. This ratio, R, is
R = -( A P h (Aph
Ordinary fluctuations in room temperature appeared to have a slight effect on the results, but not enough to causeserious errors. Good checks could bc obt,ained a t temperat,ures differing by as much as 10" F. RESULTS
T h e results of many tests of tornary mixtures containing hydrogen, methane, and carbon dioxide are expressed graphically in Figure 3, in whioh R is the ordinate, while the percentage of hydrogen in the ternary (Hx)is the abscissa.
Figure 2.
I n order to find the unknown composition of a ternary mixture, ley a st,raightedge parallel to the horizontal axis, s o that the ordinate is intersected a t the value of R determined expenmentally for the two mixtures. Xow move along the straightedge until the first curved line is interseoted. Vertioally above this point of intersection will he found the percentage of carbon dioxide in the unknown ternary. Next continue along the straightedge until that curved line is int,ersected which corresponds to the percentage of hydrogen in the methane-hydrogen mixture (Hca,). The percentage of hydrogen in the ternary (Hx) can then be rcad directly from the graph by dropping vertically from this point of intersection to the horizontal axis. The methane in the ternary is obt,nincd by difference.
Photograph of Apparatus
1'
a
PERCENT
HYDROGEN
Figure 3.
Suooose that a tornarv mlxture of unknown comuosition is drawyinto one of the burets and brought to atmospheric pressure by means of the mercury leveling bulb. A given volume of methane is then put into the other buret and hydrogen is added in small quantities. The gases are mixed thoroughly, and the deflection of the null-point indicator is observed. If the deflection of the indicator is zero when atmospheric pressure prevails in both burets, the percentage of hydrogen in the methane ( H C 4 ) is estimated from the volumes sddod. This means t h a t the filaments in the two cells are losine heat a t the same rate, owing to the combined effect of coGduction and convection a t atmospheric pressure. The next step is to reduce the pressure in the teruary'mixture by lowering the mercury bulb. This operation unbalances the bridge to an extent depending on the change in pressure, which can be called ( A P ) , . The bridge is noti balitnced once more by
IN
TEF
Nomograph
COBCLUSION S
while the ternary invest,igated in this nark coniisted only of hydrogen, carbon dioxide, and methane, the method should be applicable to ot,her combinations of gase's that do not react chemically with one another, such as the commercially im~t portant mixture f, hydrogt+n,carbon and is not necessary that hydrogen be present in the ternary in order
11, UI~ITVIVVL\.
YLW~UWS
YA
.xvv.L~y
I 1111111,
llll.
471-7. New York, Merornillan Co.. 1922. (2) Gregory and Archer, P m R o y . Soc., llOA, 91 (1926); Phil. M n g . . l ( 7 ) . 593 (1926).
