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Page 6
If I am justified in taking this view, then I am justified in applying
to my heat engine the general principles laid down in 1824 by Sadi
Carnot, namely, that the proportion of work which can be obtained out
of any substance working between two temperatures depends entirely and
solely upon the difference between the temperatures at the beginning
and end of the operation; that is to say, if T be the higher
temperature at the beginning, and _t_ the lower temperature at the end
of the action, then the maximum possible work to be got out of the
substance will be a function of (T-_t_). The greatest range of
temperature possible or conceivable is from the absolute temperature
of the substance at the commencement of the operation down to absolute
zero of temperature, and the fraction of this which can be utilized is
the ratio which the range of temperature through which the substance
is working bears to the absolute temperature at the commencement of
the action. If W = the greatest amount of effect to be expected, T and
_t_ the absolute temperatures, and H the total quantity of heat
(expressed in foot pounds or in water evaporated, as the case may be)
potential in the substance at the higher temperature, T, at the
beginning of the operation, then Carnot's law is expressed by the
equation:
/ T - t \
W = H( ------- )
\ T /
I will illustrate this important doctrine in the manner which Carnot
himself suggested.
[Illustration: THE GENERATION OF STEAM. Fig 2.]
Fig. 2 represents a hillside rising from the sea. Some distance up
there is a lake, L, fed by streams coming down from a still higher
level. Lower down on the slope is a millpond, P, the tail race from
which falls into the sea. At the millpond is established a factory,
the turbine driving which is supplied with water by a pipe descending
from the lake, L. Datum is the mean sea level; the level of the lake
is T, and of the millpond _t_. Q is the weight of water falling
through the turbine per minute. The mean sea level is the lowest level
to which the water can possibly fall; hence its greatest potential
energy, that of its position in the lake, = QT = H. The water is
working between the absolute levels, T and _t_; hence, according to
Carnot, the maximum effect, W, to be expected is--
/ T - t \
W = H( ------- )
\ T /
/ T - t \
but H = QT [therefore] W = Q T( ------- )
\ T /
W = Q (T - t),
that is to say, the greatest amount of work which can be expected is
found by multiplying the weight of water into the clear fall, which
is, of course, self-evident.
Now, how can the quantity of work to be got out of a given weight of
water be increased without in any way improving the efficiency of the
turbine? In two ways:
1. By collecting the water higher up the mountain, and by that means
increasing T.
2. By placing the turbine lower down, nearer the sea, and by that
means reducing _t_.
Now, the sea level corresponds to the absolute zero of temperature,
and the heights T and _t_ to the maximum and minimum temperatures
between which the substance is working; therefore similarly, the way
to increase the efficiency of a heat engine, such as a boiler, is to
raise the temperature of the furnace to the utmost, and reduce the
heat of the smoke to the lowest possible point. It should be noted, in
addition, that it is immaterial what liquid there may be in the lake;
whether water, oil, mercury, or what not, the law will equally apply,
and so in a heat engine, the nature of the working substance, provided
that it does not change its physical state during a cycle, does not
affect the question of efficiency with which the heat being expended
is so utilized. To make this matter clearer, and give it a practical
bearing, I will give the symbols a numerical value, and for this
purpose I will, for the sake of simplicity, suppose that the fuel used
is pure carbon, such as coke or charcoal, the heat of combustion of
which is 14,544 units, that the specific heat of air, and of the
products of combustion at constant pressure, is 0.238, that only
sufficient air is passed through the fire to supply the quantity of
oxygen theoretically required for the combustion of the carbon, and
that the temperature of the air is at 60� Fahrenheit = 520� absolute.
The symbol T represents the absolute temperature of the furnace, a
value which is easily calculated in the following manner: 1 lb. of
carbon requires 2-2/3 lb. of oxygen to convert it into carbonic acid,
and this quantity is furnished by 12.2 lb. of air, the result being
13.2 lb. of gases, heated by 14,544 units of heat due to the energy of
combustion; therefore:
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