Join T by
another diagonal with extremity of the heating surface on the zero
line, then the larger triangle, standing on the zero line, will
represent the whole of the heat of combustion, and the ratio of the
two triangles will be as the lengths of their respective bases, that
is, as (T - _t_) / T, which is the expression we have already used. The
heating surface was 220 square feet, and it was competent to transmit
the energy developed by 41 lb. of coal consumed per hour = 12,819 u. x
41 u. = 525,572 units, equal to an average of 2,389 units per square
foot per hour; this value will correspond to the mean pressure in an
ordinary diagram, for it is a measure of the energy with which
molecular motion is transferred from the heated gases to the
boiler-plate, and so to the water. The mean rate of transmission,
multiplied by the area of heating surface, gives the area of the
shaded portion of the figure, which is the total work which should
have been done, that is to say, the work of evaporating 544 lb. of
water per hour. The actual work done, however, was only 485 lb. To
give the speculations we have indulged in a practical turn, it will be
necessary to examine in detail the terms of Carnot's formula. Carnot
labored under great disadvantages. He adhered to the emission theory
of heat; he was unacquainted with its dynamic equivalent; he did not
know the reason of the difference between the specific heat of air at
constant pressure and at constant volume, the idea of an absolute zero
of temperature had not been broached; but the genius of the man, while
it made him lament the want of knowledge which he felt must be
attainable, also enabled him to penetrate the gloom by which he was
surrounded, and enunciate propositions respecting the theory of heat
engines, which the knowledge we now possess enables us to admit as
true.
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