CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES
11.6 ADIABATICFLAMETEMPERATURE 341
constitute a univariant subsystem that at constant pressure is at the fixed temperature of
the equilibrium phase transition. The thermal energy released or absorbed by the reaction,
instead of changing the temperature, is transferred isothermally to or from the coexisting
phases and can be measured by the volume change of the phase transition. A reaction en-
thalpy, of course, can only be measured by this method at the temperature of the equilibrium
phase transition. The well-known Bunsen ice calorimeter uses the ice–water transition at
0 C. The solid–liquid transition of diphenyl ether has a relatively large volume change and
is useful for measurements at26:9C. Phase-transition calorimeters are especially useful
for slow reactions.
Aheat-flow calorimeteris a variation of an isothermal-jacket calorimeter. It uses a ther-
mopile (Fig.2.7) to continuously measure the temperature difference between the reaction
vessel and an outer jacket acting as a constant-temperature heat sink. The heat transfer takes
place mostly through the thermocouple wires, and to a high degree of accuracy is propor-
tional to the temperature difference integrated over time. This is the best method for an
extremely slow reaction, and it can also be used for rapid reactions.
Aflame calorimeteris a flow system in which oxygen, fluorine, or another gaseous
oxidant reacts with a gaseous fuel. The heat transfer between the flow tube and a heat sink
can be measured with a thermopile, as in a heat-flow calorimeter.
11.6 Adiabatic Flame Temperature
With a few simple approximations, we can estimate the temperature of a flame formed in
a flowing gas mixture of oxygen or air and a fuel. We treat a moving segment of the gas
mixture as a closed system in which the temperature increases as combustion takes place.
We assume that the reaction occurs at a constant pressure equal to the standard pressure,
and that the process is adiabatic and the gas is an ideal-gas mixture.
The principle of the calculation is similar to that used for a constant-pressure calorimeter
as explained by the paths shown in Fig.11.11on page 334. When the combustion reaction
in the segment of gas reaches reaction equilibrium, the advancement has changed byÅ
and the temperature has increased fromT 1 toT 2. Because the reaction is assumed to be
adiabatic at constant pressure,ÅH(expt) is zero. Therefore, the sum ofÅH.rxn; T 1 /and
ÅH.P/is zero, and we can write
ÅÅcH.T 1 /CZT 2
T 1Cp.P/dT D 0 (11.6.1)whereÅcH.T 1 /is the standard molar enthalpy of combustion at the initial temperature,
andCp.P/is the heat capacity at constant pressure of the product mixture.
The value ofT 2 that satisfies Eq.11.6.1is theestimatedflame temperature. Problem
- 9 presents an application of this calculation. Several factors cause the actual temperature
in a flame to be lower: the process is never completely adiabatic, and in the high temperature
of the flame there may be product dissociation and other reactions in addition to the main
combustion reaction.