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In practice, the adiabatic expansion of steam-like vapors may be approximately realized, but there is well-nigh an insuperable difficulty in securing the adiabatic expansion of saturated ether-like vapors : for, in the former case, if steam be in the state of saturation at the instant of the cut-off, it will continue to be saturated during expansion; but, with the latter, if no ether liquid be present at the instant of cut-off, the vapor will superheat during expansion, and instead of realizing equation (a), the curve of expansion will be of the form

p = a constant,

in which will be the ratio of the specific heat at constant pressure to that at constant volume, but probably will not be 1.405 as for perfect gases. We will continue to consider the vapor as saturated. To find the work done during adiabatic expansion, let x be so much less than unity that the vapor will remain saturated throughout expansion, then will

U1 = AEFD =SGH. dp = JS [c log

Τι

T

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If, in this expression, the value of a from equation (a) be substituted, and subscript, be attached to those variables which are without subscripts, we will have

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the former of which, equation (k), is better adapted to the discussion of steam-like vapors, and equation (7) to ether-like vapors; for in the former x1 may be unity, and in the latter 2 may be unity.

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in which for steam-like vapors x, may be unity, but x, must be less than unity; and, on the contrary, for ether-like vapors x may be unity, but less than unity.

If, during the return stroke, the fluid be refrigerated so as to maintain the constant temperature, the pressure will be uniform and equal OD; and if at some point, as J, adiabatic compression begins and is continued until the temperature is raised to 71 at A, let x, be the weight of vapor at state A, then will the work done by compression be found by simply changing x1 to æ, since all the other quantities remain as before:

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hence the work done in the cycle AEFJA will be

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which is the same as that of the perfect elementary engine.

To find the work done during adiabatic expansion when the initial state A is that of liquid only, make x, 0 in the value of Us, or 1 = 0 in equation (k), giving

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Actual engines do not expand down to the back pressure, neither is the pound of fluid retained in the cylinder; but at the end of the expansion the exhaust is opened, and the vapor escapes until the exhaust is closed at the point L in the back stroke. The adiabatic

AL will then be for only a fraction of a pound. Neglecting compression and clearance, we have

U = ABCNMA = ABCD+ (P2 — P3) X2 V2,

where P2 = OD, Ps

=

OM, absolute pressures. If ΤΑ perature of the feed water, the heat supplied will be

be the tem

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From this result it appears that in the case of actual engines, the specific heat of the working fluid and the latent heat of evaporation both affect the efficiency. If the feed water be at the temperature of the exhaust, then 7, 72, and the preceding expression may be reduced to

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a form not new. By retaining x and x2, equation (p) is applicable both to "steam-like" and "ether-like" vapors, only observing that neither nor can exceed unity, and that they are related to each other through equation (a).

DISCUSSION.

Prof. Denton.-Prof. Wood, in this last paper, has gone into a great many computations about the liquefaction of steam from the theoretical standpoint, which are certainly very interesting to the student. I believe he has carried them much farther than any previous writer. As a little contribution to the practical value of these computations for steam-engine practice, I am minded to tell a story about a card. I see two gentlemen in this

room who will probably recall having seen it before, but perhaps the rest have not. A few years ago very few people had noticed this fact. Suppose we have an indicator card cutting off at about one-fifth in an ordinary non-condensing engine, so as to expand say to the atmospheric line, say from 80 pounds boiler pressure. Now, such a card will have a mean effective pressure of somewhere around 25 pounds. I have trusted to my memory for that. Then the work we get out of the steam is this 25 pounds to the square inch times 144 pounds, times the volume of this steam, which is somewhere about 26 cubic feet. That will be the foot-pounds of work we get out of that card for a pound of steam. Without going into it too fine, it is somewhere about ninety thousand foot-pounds. Now, it was as I say, some years back, a common idea, and I had it myself, that this heat was accounted for by the difference of heat in the steam. The total heat of steam at 80 pounds is somewhere around 1210 thermal units. At atmospheric pressure it is 966+212, or about 1180. The difference is only 25 thermal units. If you multiply by Joule's equivalent to get it into foot-pounds, we have about 20,000 footpounds accounted for, against 90,000 of actual work, by the card. Therefore the heat which the steam contains at the higher pressure less the heat that it contains at the lower pressure does not begin to account for the work we know we get from the actual indicator card. Unless this theory of liquefaction comes to our aid, there is no possible explanation for it. This theory of liquefaction, you observe, does not depend upon cylinder condensation at all. Suppose this is absolutely a non-conducting cylinder, then, by these theories which Prof. Wood has reviewed so ably, it turns out that by adiabatic expansion alone ten per cent. of the fluid liquefies and gives up all its latent heat in order that the rest may remain vaporous steam. Now, ten per cent. of that latent heat is 90 thermal units, which multiplied by the 772 gives us about 70,000. This,* added to the 20,000, gives us what we get from the card, viz., 90,000 ft. lbs. But you see, unless we have this theory of liquefaction, we do not begin to account for what occurs at all. This liquefaction by the adiabatic expansion was a great discovery. That was the situation of steam-engines probably most of us know at the time of Regnault's experiments. Regnault's experiments were waited for by everybody all over the scientific world. These theories of liquefaction had not been perfected.

*The exact calculation is given in the Am. Engineer, Nov. 7th, 1884.

When Regnault's experiments were published, scientists immediately put this sort of computation against the actual steamengine measurement, and it did not begin to account for the actual performance of steam-engines. The German experimenter Hirn had measured steam-engines and found that they did give these 90,000 units between these two points, and theory only accounted, by Regnault's experiments, for the 20,000 units, and it was under the stimulus of this discrepancy that Rankine and Clausius discovered these mathematical laws of liquefaction and brought the two facts together.

By arrangement with Prof. Wood, I offer the following practical deductions regarding volatile vapor engines, based upon such equations as his paper discusses.

The computation of the table is to be credited to Prof. D. S. Jacobus, of Hoboken.*

It applies to engines whose indicator cards would be like the accompanying figure (Fig. 210), EA representing clearance volume, the compression line DA being arranged to compress to boiler pressure before the valve opens for admission, and the terminal pressure being that of the atmosphere, with the point of release assumed at exactly the end of the stroke.

Under these conditions, the influence of clearance on economy is entirely eliminated, and if the efficiency be computed without regard to cylinder condensation, we shall obtain the maximum economy that can be expected to be realized between the pressures chosen, and yet we shall have introduced no condition inconsistent with the use † of a vapor in a modern high-pressure engine. Column 7 of the table expresses the fraction of the heat in the vapor (when it enters the working cylinder) which is realized as work, or which is represented by the indicated horse-power computed from the diagram ABCDA. It will be seen that these fractions are practically the same for all the vapors. Leaving the air out of consideration for the present, let us consider the reason for this absence of difference of economy of the vapors, notwithstanding that there is so much difference in their boiling points, latent heat, etc.

*. Efficiency of Vapor Engines," Stevens Indicator, Oct., 1888.

The latest applications of bisulphide of carbon, ammonia, etc., as a motive fluid, do not afford a back pressure practically less than the atmosphere, notwithstanding a condenser is used. For this reason, Prof. Jacobus confines his calcu lations to the diagram which exhausts against a pressure equal to that of the atmosphere.

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