If the theory and observations were correct, the values of a should all be the same, but perfect agreement is not to be expected.

The value 86.1 is larger than that found on the condition that steam is a perfect gas composed of two permanent gases, hydrogen and oxygen; for at the pressure of one atmosphere we have:

This being ideal steam at 32° F., we have for the volume of one cubic foot of ideal steam at 32° F., under one atmosphere:

greater than the ideal value, or about of one per cent. greater. The value of a, found by the writer for actual steam at 212° F., is 83.37, which is 2 per cent. less than the value for ideal steam (Thermodynamics, p. 103).

The hypothesis, then, of equation (8) is satisfactory for steam at and above the state of saturation, and the writer has shown in his

Thermodynamics (2d ed., p. 312), that a1 =

equation for steam being

do

α

very nearly, the

Regnault's experiments show that pv for ammonia diminishes with diminution of volume, the same as for steam; so we assume the equation

b

(10)

To find the constants in this equation, we resort to the experi ments of Regnault.

TABLE III.

Results of Regnault's experiments on the elasticity of Ammonia Gas. The temperature of the water surrounding the tube containing the gas was 8.1° C. (46.58° F.).

In determining the ratio of pe to p'v', Regnault chose those experiments in which the pressure of the larger was about double that of the smaller, and this is why 703 was used instead of 668. The products pv in the last column are one-tenth their actual value, but no error results in the ratio on this account. The marks on the scale differ by equal increments, and the volumes decrease by nearly constant increments, the mean for the entire range being 41.55; but the pressures increase by increasing incre

ments.

If the products pv were constant, the gas would be perfect. The pressures and relative volumes determine points in the isothermal AC, Fig. 208, of this gas for the temperature 8.1° C. (46.58 F.). The line AB represents the isothermal of a perfect gas passing through A, the temperature of which would be somewhat

B

Fig. 208

less than that of AC, since the two isothermals will be asymptotic to each other at an indefinite distance to the right, and hence for the same temperature both cannot pass through the common point A. The pressure at A will be 668.93 mm., and at C 1435.33 mm., according to the preceding table; the relative volume Ov will be 841.95, and Ov', 384.89. The equation of the isothermal AB of a perfect gas passing through A will be

pv668.93 × 841.95 r = 5632.50 7.

The ordinate DB will be

A

D

E

ບ

hence, through a range of pressures of 1435.33 - 668.93766.40 mm., or more than one atmosphere, the pressure falls below that for a perfect gas nearly 2 per cent.

We may now find the superior limit of the latent heat at the

volume

v=

718.07 1435.33

× 20.7985 = 11.15 (nearly),

as shown hereafter; for it will be the value in equation (8) divided by 1.01881, or,

In Fig. 207 let a be the state representing the atmospheric pressure, 760 mm., at the temperature of melting ice, 0°C.; then will the volume oh be 20.7985 cubic feet for one pound, as found above. We now find the pressure at state b on the isothermal 8.1° C. for the same volume, and since the gas will be superheated at a

and all temperatures above, the law of perfect gases will hold almost exactly for this distance, and we have

pounds per square foot. In millimeters this will be

which value is entered in a parenthesis in Table III. Regnault made an observation at a pressure of 783.18 mm. a pressure exceeding that at b by only 0.70 mm.-the relative volume corre

sponding to which, assuming that the volumes and pressures change uniformly between consecutive observations, will be 718.07, which value is entered in Table V., in a parenthesis, and also the corresponding product pv = 561.870. The actual volume at b is 20.7985 cubic feet, and the volumes per pound for all the twelve experiments of Table V. may be found by multiplying the relative 20.7985 ; and the pressures in pounds per square foot 718.07

volumes by

will be the millimeters multiplied by

2116.3
760

These operations

give the following table:

TABLE IV.

Results of Regnault's experiments upon the elasticity of Ammonia Gas at the constant temperature of 46.58° F., reduced to English units.

The numbers in the parentheses are interpolated.

The pressure at b is only 0.43 of a pound higher than at a, so that the error, if any, in assuming the law of perfect gases through this amount, will scarcely be perceptible.

For state whose volume is 18.365, we have

pv = 2458.80 × 18.365 = 45196 ft. lbs. ;

for state 8, representing the first experiment in Table VI., pv 1862.70 × 24.3716 = 45397 ft. lbs.;