with increase of volume; then, if c be the specific heat of the

Differentiating equation (22), after which dropping the subscripts, since the inferior limit is arbitrary and may coincide with DC, then

For T-40° F., 24.372; .. c = 1.091,

According to formula (24) the specific heat decreases with increase of temperature, a principle which is true of water from 40° F. to about 80° F. This computation assumes that the behavior of the liquid and vapor conforms exactly with the laws assumed; a condition which rarely, if ever, exists. It will therefore be advisable, for engineering purposes, to assume that the specific heat is constant, at least until the experimental value is determined, and equal to that of water-or unity. The results from 0° to 100°, generalized, become

c = 1.096.0012 T nearly.

(25)

The following table has been computed from these formulas:

The President, H. R. Towne.-The increasing use of ammonia machines makes data of this kind exceedingly valuable and interesting.

Prof. Denton.-I might say that this experiment on an ice machine that I reported last evening affords data to confirm a

figure somewhere near to 580. This is the latent heat of ammonia at low pressure and low temperature. But unfortunately for the higher pressure I do not dare to say that the experiment affords a check, but the 580 or thereabouts is entirely confirmed by my experiment on a large scale, and I shall show it up in the appendix. The reason I cannot give the latent heat in the higher pressures is because it depended upon the measurement of water, and it will be seen from my paper that that is not done with the same accuracy as the brine, so that I shall not commit myself with a figure for latent heat until I have a chance to verify it. I would like to say that arrangements are now almost perfected to determine the latent heat in the laboratory, and I expect to be able to help Prof. Wood out on it in an experimental way before long.

Prof. Wood.--It will be a satisfaction to have the constants of ammonia re-determined experimentally, but I have so much confidence in the correctness of Regnault's experiments and of the application of the theory of gases, that I will question experimental results that differ much from those here given within the volumes experimented upon by Regnault; that is, between 10 and 25 cubic feet per pound. Where the volume is 11.3 cubic feet, the temperature of saturation will be about 10° F. below zero, and the latent heat of vaporization about 560 B. T. U. Equation (12) will give more accurate results than equation (14), although the latter is made to pass through three states of the former. Ledoux found for the latent heat of vaporization when given in British units,

he 583.33 0.5499 T 0.0011737,

=

and this compared with equation (12) above, shows that our equation, within working limits, gives smaller values than Ledoux, and that it decreases more rapidly with increase of temperature.

CCCXLIII.

SOME PROPERTIES OF VAPORS AND VAPOR

ENGINES.

BY DE VOLSON WOOD, HOBOKEN, N. J.

(Member of the Society.)

By vapors we mean saturated vapors, or such as have a definite pressure for a given temperature independent of their volume. We propose to consider cases in which there is a mixture of vapor and its liquid, discarding, however, the volume of the liquid, and in case of the engine discarding clearance and compression. Rankine, Clausius, and others have solved some cases under those restrictions, but their results are not generally applicable alike to vapors having specific heats of opposite signs. We propose to generalize the expressions, and possibly give some new properties of adiabatics.

E

B

Consider only one pound of fluid in the cylinder, and let BC be the curve of saturation, and EF any adiabatic in which there is only a fraction of the pound that is vapor throughout the expansion.

K

G

D

M

O

H

Fig. 150.

N

AB (Fig. 150) will represent the vol ume of a pound of vapor at the absolute pressure OA = p, and absolute temperaand pressure

ture T, GI the volume at the absolute temperature

Let x1 = AE÷AB = the fractional part of the pound at the

state E

V1 = AB, x1 v1 = AE.

* = GH : GI

V = GI, x v = GH.

he, the latent heat of evaporation at temperature 7 in ordinary heat units, which will be

he, at temperature 71, and

c, the specific heat of the liquid.

in which 70 is any arbitrary temperature. Since the vapor is to be continually saturated, this equation is limited to the conditions that 1 must not be negative, and must be less than 1, and at the same time X, for any amount of expansion, must be less than 1.

Let subscript, be used for the terminal state F, then,

The difference between the initial and terminal weights of vaj or will be

and this may be negative, zero, or positive. Rankine and Clausius independently discovered the fact that steam condensed when expanded adiabatically, and that this is true for all vapors the specific heat of whose saturated vapors are negative, and the reverse for those which are positive. The former we will designate as "steam-like vapors," and the latter as "ether-like vapors "-steam and ether being typical of their respective classes.

The principle stated by these eminent writers is known to be correct both by theory and experiment-when the initial state is that of pure saturated vapor; but when liquid is present with the vapor in the initial state, it may not be true, for we will show that, with steam-like vapors, evaporation, instead of condensation, may take place during some part of adiabatic expansion. This is best shown numerically. Let the fluid be water, then c x=0.436 at 800° F. (absolute), he 7 =

=

1436.8

= 1, and let 0.7 T. Then