## The Cambridge and Dublin Mathematical Journal, Volumen5 |

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Página 254 - 087 feet. Hence the work developed during an entire stroke is •087 xp foot-pounds. Now this is developed by the descent from 0° to - f of the quantity of heat necessary to melt a cubic foot of ice; that is, by 4925 thermic units, the unit being the quantity of heat required to raise a pound of water from 0° to 1° centigrade.

Página 249 - ... water is subjected is increased. The following is the reasoning by which these conclusions are proved. First, to prove that water at the freezing point may be converted into ice by a process solely mechanical, and yet without the final expenditure of any mechanical work : — Let there be supposed to be a cylinder, and a piston fitting water-tight to it, and capable of moving without friction. Let these be supposed to be formed of a substance which is a perfect non-conductor of heat ; also, let...

Página 255 - ... 087 x p. Hence t = -00000355^ .............. (1). This, then, is the desired formula for giving the freezing point - t° centigrade, which corresponds to a pressure exceeding that of the atmosphere by a quantity p, estimated in pounds on a square foot. To put this result in another form, let us suppose water to be subjected to one additional atmosphere, and let it be required to find the freezing point. Here p = one atmosphere = 2120 pounds on a square foot; and therefore, by (1), t = -00000355...

Página 248 - THOMSON. (Taken, with some slight alterations made by the author, from the Transactions of the Royal Society of Edinburgh, vol. xvi. part v. 1849.) SOME time ago my brother (Professor "William Thomson) pointed out to me a curious conclusion to which he had been led, by reasoning on principles similar to those developed by Carnot, with reference to the motive power of heat. It was, that water at the freezing point may be converted into ice by a process solely mechanical, and yct without the final...

Página 253 - Place the bottom of the cylinder in contact with a second indefinitely large lake at — f, and move the piston upwards. During this motion the pressure must remain constant at p above that of the atmosphere, the water in the cylinder increasing its volume by freezing, since if it did not freeze, its pressure would diminish, and therefore its temperature would increase, which is impossible, since the whole mass of water and ice is constrained by the lake to remain at —t°. Continue the motion till...

Página 254 - ... which represents the work developed by the engine during one complete stroke, and this can readily be obtained with sufficient accuracy. For, even though we should adopt a very large value for fm, the change of pressure during Process 2, still the changes of volume gm and hn in Process 2 and Process 4 would be ex'tremely small compared to the expansion during the freezing of the water; and from this it follows evidently that the area of the figure efgh is extremely nearly equal to that of the...

Página 252 - The effect of the motion of the piston is to convert ice at 0° into water at 0°, and to abstract from the lake at 0° the heat which becomes latent during this change. Continue the compression till one cubic foot of water is melted from ice. Process 2. Remove the cylinder from the lake, and place it with its bottom on a stand which is a perfect non-conductor of heat. Push the piston a very little farther down, till the pressure inside is increased by any desired quantity which may be denoted, in...

Página 253 - ... above that of the atmosphere, the water in the cylinder increasing its volume by freezing, since if it did not freeze, its pressure would diminish, and therefore its temperature would increase, which is impossible, since the whole mass of water and ice is constrained by the lake to remain at —t°. Continue the motion till so much heat has been given out to the second lake at — t", as that if the whole mass contained in the cylinder were allowed to return to its original volume without any...

Página 249 - Carnot, with reference to the motive power of heat. It was, that water at the freezing point may be converted into ice by a process solely mechanical, and yet without the final expenditure of any mechanical work. This at first appeared to me to involve an impossibility, because water expands while freezing...

Página 253 - Process 1. At the end of this fourth process the mass contained in the cylinder must, according to the condition by which the termination of Process 3 was fixed, have its original temperature and pressure, and therefore it must be in every respect in its original physical state. By representing graphically in a diagram the various volumes and corresponding pressures, at all the stages of the four processes which have just been described, we shall arrive, in a simple and easy manner, at the quantity...