The steam engine considered as a thermodynamic machine: a treatise on the thermodynamic efficiency of steam engines, illustrated by diagrams, tables, and examples from practice by Cotterill James Henry 1836-1922

Author:Cotterill, James Henry, 1836-1922
Language: eng
Format: epub
Tags: Thermodynamics, Steam-engines
Publisher: London, New York, E. & F. N. Spon
Published: 1890-03-25T05:00:00+00:00

The efficiency of this engine is now to be found by comparing it with an air engine, which receives and rejects heat in the same way. In Fig. 27b the diagram of such an engine is shown: M A represents a rise of pressure at constant volume diuing reception of heat, A B &n increase of volume at constant temperature during a further application of heat, B C expansion without gain or loss of heat till temperature has fallen to that of the refrigerator, C M compression at constant temperature till the air has returned to its original state. Dififerent as the two diagrams may appear on paper, yet from a thermodynamical point of view they are precisely similar, provided the temperatures be the same, and the quantities of heat supplied at each temperature be in the same proportion : hence the efficiency of the two engines must be the same according to the generalised form of Camot's principle given in Art. 93.

Now in the air engine the heat expended or rejected at each step of the process is, employing the notation of Chapter lY., per lb. of air.

During elevation of temperature ^„ (Tj - T^

„ expansion cT-^ log^ r

„ compression cTq log^ R

where I\, T^ are the temperatures at which the air receives and rejects heat during its expansion A B and compression C M At

constant temperatures, r, B, the ratios of expansion and compression (Isothermal).

In the steam engine, on the other hand, the heat expended per lb. of steam is

During elevation of temperature T^ T^

„ evaporation ^^i

„ condensation Xo^o

where 1 - a^, 1 - x© *^® *^® weights of water mixed with the steam at the beginning and end of the expansion respectively, and L^y Lq are as usual the latent heats of evaporation at J\, T^.

We must now suppose the air engine so arranged that the quantity of heat received at constant temperature is in the same proportion to that received at constant volume as in the case of the steam engine, that is to say, we must suppose

c T^ logg r gi A

but by Art. 31, page 82.

^ =v 1-

•• (y - 1)3^1-log, r. =»iZri.

This condition being satisfied, the air engine and the steam engine will receive heat, at the same temperatures, in the same proportions, which is the needful condition that the efficiency may be the same : thus it will necessarily follow that the heat rejected in the two cases is in that same proportion, so that by similar reasoning

but) if / be the ratio of adiabatic expansion in the air engine, it is clear that

And by Art 36 we know that

-(^y^-

T (y - l)log«r' =logcy^

0

and

T (y - 1) logc jB = (r - l)log€r + loge ^ ;

whence replacing (y - 1) log^ r, (y - 1) log^ B by their values just given, it is clear that

^-#«=^+log.^ (I)

97. The method employed in the last article is based on the first statement of Art. 93, page 207. It is very instructive as an

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