Page 403 - Instrumentation Reference Book 3E

386 Chemical analysis: gas analysis

Table 18.1 Relative thermal conductivities of some cylindrical hole is filled with the gas under test.
common gases The temperature of the wire reaches an equilib-
rium value when the rate of loss of heat by
Gas Colmduciiviiy conduction, convection, and radiation is equal to
Air 1.00 the rate of production of heat by the current in
Oxygen 1.01 the wire. In practice, conduction through the gas
Nitrogen 1 .oo is the most important source of heat loss. End-
Hydrogen 4.66 cooling, convection, radiation, and thermal diffu-
Chlorine 0.32 sion effects, though measurable, account for so
Carbon monoxide 0.96 small a part (less than 1 percent each) of the total
Carbon dioxide 0.59 loss that they can satisfactorily be taken care of in
Sulphur dioxide 0.32 the calibration. Most instruments are designed to
Water vapor 1.30 operate with the wire mounted vertically, to mini-
Helium 4.34
mize losses by convection. Convective losses also
increase with the pressure of the gas, so the pres-
sure should be controlled for accurate conductiv-
where KO is the thermal conductivity at 0 “C and b ity measurements in dense gases. The heat loss
is a constant. from the wire depends on the flow rate of gas in
The relative thermal conductivities of some
gases, relative to air as 1.00, are given in Table the sensor. In some instruments errors due to
changes in gas flow are minimized because the
18.1. gas does not flow through the cell but enters by
It can be shown that the conductivity of a
binary mixture of gases is given by diffusion, but otherwise the gas flow rate must be
carefully controlled.
One must also be mindful that in the case of
gases, mass flow is also a function of pressure. At
pressures typically used in analyzers the relation-
ship between the change in volume as a function
where A and B are constants known as the Wasil- of pressure can be approximated by the ideal gas
jewa constants, Kl and K2 are the conductivities of law or PI VI = P2Vz.
the pure gases, and x1 is the molar fraction of The resistance of the wire depends on its tem-
component 1. perature; thus, by measuring the resistance of the
In gas analysis, conductivities of pure gases are wire, its temperature may be found, and the wire
of limited value, and it is much more important to is effectively used as a resistance thermometer.
know how the conductivity of a mixture varies with The electrical energy supplied to the wire to main-
the proportion of the constituent gases. However, tain the excess temperature is a measure of the
as shown above, th:: relationship between the total heat loss by conduction, convection, and
conductivity of a mixture of gases and the propor- radiation. To measure the effects due to changes
tion of the constituents is complicated. When colli- in the conductivity of the gas only, the resistance
sions occur between molecules of different gases the of the hot wire in a cell containing the gas to be
mathematics of the collisions are no longer simple, tested is compared with the resistance of an
and the relationship between conductivity and the exactly similar wire in a similar cell containing a
proportions of the constituents depends upon the standard gas. This differential arrangement also
molecular and physical constants of the gases, and lessens the effects of changes in the heating cur-
on the intermolecular forces during a collision. In rent and the ambient temperature conditions. In
practice thermal conductivity instruments are order to increase the sensitivity two measuring
therefore calibrated by establishing the required and two reference cells are often used, and this
composition-conductivity curves experimentally. arrangement is usually referred to as a “katha-
Several forms of gas sensor based on thermal rometer.”
conductivity have been developed. The majority In the katharometer four filaments with pre-
use the hot-wire method of measuring changes in cisely matched thermal and electrical characteris-
conductivity, with the hot-wire sensors arranged tics are mounted in a massive metal block, drilled
in a Wheatstone bridge circuit. to form cells and gas paths. A cutaway drawing
of a 4-filament cell is shown in Figure 18.3.
18.3.1.1 Katharometev Depending on the specific purpose, the filaments
may be made of tungsten, tungsten-rhenium
A wire, heated electrically and maintained at con- alloy, platinum, or other alloys. For measure-
stant temperature, is fixed along the axis of a ments in highly reactive gases gold-sheathed
cylindrical hole bored in a metal block which is tungsten filaments may be used. The filaments
also maintained at a constant temperature. The are connected in a Wheatstone bridge circuit,