From this table it appears, that, for every tenth of an inch which the barometric column varies between these limits, the boiling temperature changes by the fraction of a degree expressed by the decimal ·176, or nearly by the vulgar fraction 1⁄6.
(63.)
Let us suppose a given weight of water at the temperature of 32° to be exposed to any regular source by which heat may be supplied to it. If it be under the ordinary atmospheric pressure, the first 180° of heat which it receives will raise it to the boiling point, and the next 1000° will convert it into steam. Thus, in addition to the heat which it contains at 32°, the steam at 212° contains 1180° of heat. But if the same water be submitted to a pressure equal to half the atmospheric pressure, then the first 148° of heat which it receives will cause it to boil, and the next 1032° will convert it into vapour. Thus, steam at the temperature of 180° contains a quantity of heat more than the same quantity of water at 32°, by 1032° added to 148°, which gives a sum of 1180°. Steam, therefore, raised under the ordinary pressure of the atmosphere at 212°, and steam raised under half that pressure at 180°, contain the same quantity of heat,—with this difference [Pg115] only—that the one has more latent heat, and less sensible heat, than the other.
From this fact, that the sum of the latent and sensible heats of the vapour of water is constant, it follows that the same quantity of heat is necessary to convert a given weight of water into steam, at whatever temperature, or under whatever pressure, the water may be boiled. It follows, also, that, in the steam engine, equal weights of high-pressure and low-pressure steam are produced by the same consumption of fuel; and that, in general, the consumption of fuel is proportional to the quantity of water vaporised, whatever the pressure of the steam may be.[18]
(64.)
Fig. 18.
Let A B ([fig. 18.]) be a tube, or cylinder, the base of which is equal to a square inch, and let a piston P move in it so as to be steam-tight. Let it be supposed, that under this piston there is, in the bottom of the cylinder, a cubic inch of water between the bottom of the piston and the bottom of the tube; let the piston be counterbalanced by a weight W acting over a pulley, which will be just sufficient to counterpoise the weight of the piston, so as leave no force tending to keep the piston down, except the force of the atmosphere acting above it. Under the circumstances here supposed, the piston being in contact with the water, and all air being excluded, it will be pressed down by the weight of the atmosphere, which we will suppose to be fifteen pounds, the magnitude of the piston being a square inch. [Pg116]
Now let the flame of a lamp be applied at the bottom of the tube; the water under the piston having its temperature thereby gradually raised, and being submitted to no pressure save that of the atmosphere above the piston, it will begin to be converted into steam when it has attained the temperature of 212°. According as it is converted into steam, it will cause the piston to ascend in the tube until all the water has been evaporated. If the tube were constructed of sufficient length, the piston then would be found to have risen to the height of about seventeen hundred inches, or one hundred and forty-two feet; since, as has been already explained, water passing into steam under the ordinary pressure of the atmosphere undergoes an increase of bulk in the proportion of about seventeen hundred to one.