( .0304)
= 14,600 × .8445 + 62,000 (.0425 - -----) + 4000 × .0091 = 14,765 B. t. u.
( 8 )
This coal, by a calorimetric test, showed 14,843 B. t. u., and from a
comparison the degree of accuracy of the formula will be noted.
The investigation of Lord and Haas in this country, Mabler in France,
and Bunte in Germany, all show that Dulong's formula gives results
nearly identical with those obtained from calorimetric tests and may be
safely applied to all solid fuels except cannel coal, lignite, turf and
wood, provided the ultimate analysis is correct. This practically limits
its use to coal. The limiting features are the presence of hydrogen and
carbon united in the form of hydrocarbons. Such hydrocarbons are present
in coals in small quantities, but they have positive and negative heats
of combination, and in coals these appear to offset each other,
certainly sufficiently to apply the formula to such fuels.
High and Low Heat Value of Fuels--In any fuel containing hydrogen the
calorific value as found by the calorimeter is higher than that
obtainable under most working conditions in boiler practice by an amount
equal to the latent heat of the volatilization of water. This heat would
reappear when the vapor was condensed, though in ordinary practice the
vapor passes away uncondensed. This fact gives rise to a distinction in
heat values into the so-called "higher" and "lower" calorific values.
The higher value, _i. e._, the one determined by the calorimeter, is the
only scientific unit, is the value which should be used in boiler
testing work, and is the one recommended by the American Society of
Mechanical Engineers.
There is no absolute measure of the lower heat of combustion, and in
view of the wide difference in opinion among physicists as to the
deductions to be made from the higher or absolute unit in this
determination, the lower value must be considered an artificial unit.
The lower value entails the use of an ultimate analysis and involves
assumptions that would make the employment of such a unit impracticable
for commercial work. The use of the low value may also lead to error and
is in no way to be recommended for boiler practice.
An example of its illogical use may be shown by the consideration of a
boiler operated in connection with a special economizer where the vapor
produced by hydrogen is partially condensed by the economizer. If the
low value were used in computing the boiler efficiency, it is obvious
that the total efficiency of the combined boiler and economizer must be
in error through crediting the combination with the heat imparted in
condensing the vapor and not charging such heat to the heat value of the
coal.
Heating Value of Gaseous Fuels--The method of computing calorific values
from an ultimate analysis is particularly adapted to solid fuels, with
the exceptions already noted. The heating value of gaseous fuels may be
calculated by Dulong's formula provided another term is added to provide
for any carbon monoxide present. Such a method, however, involves the
separating of the constituent gases into their elementary gases, which
is oftentimes difficult and liable to simple arithmetical error. As the
combustible portion of gaseous fuels is ordinarily composed of hydrogen,
carbon monoxide and certain hydrocarbons, a determination of the
calorific value is much more readily obtained by a separation into their
constituent gases and a computation of the calorific value from a table
of such values of the constituents. Table 37 gives the calorific value
of the more common combustible gases, together with the theoretical
amount of air required for their combustion.