136 



SCIENCE. 



[Vol. XIX. No. 474 



heating effect of the cylinder. Tbese results were strongly com- 

 bated by Professor Ferrel in Science, Vol. XVI.. pp. 192 and 193, 

 and also ,by Professor Marvin. Professor Ferrel publislied the 

 well-known thermo dynamic formula, given in Science for Feb. 

 19, and applying it to the heating in the above case found it 43° 

 F. instead of the 4° found by the exferiment. It would seem, 

 however, that these experiments had not been controverted, and 

 it is probable that their justness may yet be established This 

 problem is far-reaching in its application, and it is for this reason 

 that it is dwelt upon at some length. 



The formula given by Professor Ferrel applies only in cases 

 where a gas is compressed directly by an external force, and when 

 all the heat developed in the work of compression is concentrated 

 in the gas. One of Joule's experiments will serve toelucidate this 

 point. He determined the mechanical equivalent of heat by im- 

 mersing the cylinder into which the air was to be compressed and 

 the compressing pump in the same water bath, and then deter- 

 mining the amount of compression and the total heat developed. 

 This shows at once the truth of the following proposition. If a 

 gas when compressed is to be raised to the temperature indicated 

 by theory, it is very essential that all the heat developed in the 

 work of compression enter it. This proposition seems self-evi- 

 dent; nevertheless, it would seem that nearly all the errors that 

 have entered the various discussions and theories regarding this 

 matter have arisen fjom a neglect of this obvious statement. 



We may analyze Joule's experiment in order to gain a clearer 

 understanding of the problem. Suppose the compressing pump 

 had been in a bath by itself, and the cylinder in another bath; 

 also that no heat was lost in the passage of the air from the pump 

 to the cylinder. Under these cu-cumstances a good deal of the 

 heat due to the action of the pump would have passed into its 

 bath, and only a small portion would have been carried by the hot 

 air into the cylinder. Let us consider that a certain definite 

 amount of heating would have taken place if all the heat had en- 

 tered the air in Joule's original experiment, the formula gives the 

 rise as 123° F. if the initial temperature of the air had been 60°, 

 and the compression was to two atmospheres. In the present in- 

 stance, however, most of the heat would have been absorbed by 

 the bath aroimd the pump, and would not have been available for 

 heating the compressed air in the cylinder. It is impossible to 

 consider that the same amount of work would have sufficed to 

 heat the water around the pump, and then would have developed 

 heat enough to raise the temperature of the air in the cylinder 

 123°. 



Again, suppose that the compressed air, before entering the cyl- 

 inder, had its temperature lowered to the outside temperature; is 

 it not plain that all the heat developed in the work of compression 

 would be disposed of, and none at all would be available for heat- 

 ing the compressed air? We see, then, that it is entuely feasible 

 to bring about certain conditions under which a gas may be greatly 

 compressed without being heated. 



Let us take two equal cylinders connected by a tube and com- 

 press the air in one. A, to three atmospheres, the air in the other, 

 B, being at atmospheric pressure. Let the air in A be at the tem- 

 perature of the outside air. On opening communication between 

 the cylinders the air in A will be slightly chilled, owing to the 

 work of imparting a certain velocity to those particles rushing 

 into B; while the air in B will be heated slightly from the impact 

 of the particles rushing out of A. All the heat due to the work 

 of compression, however, will have disappeared, and none will be 

 available for heating the air in B (See Enc. Brit , Vol. XXIl.. p. 

 480, section 84). 



Lastly, suppose that the air in A should be allowed to escape 

 into the open air; the resistance to the rush of the air would be 

 much less than in the last case, and hence a greater velocity 

 would be imparted to the particles rushing from A, and the cooling 

 would he slightly greater than before. The situation appears very 

 plain, and there is no difficulty now in understanding why the ear- 

 lier experimental heating and cooling was only 4°. 



These views seem almost startling in their nature, and if true 

 certainly have profound significance. Let us try to picture the 

 real condition of the gas when under compression and flowing 

 from one reservoir to another. The confined air has a certain po- 



tential energy and a capacity for work; it may flow into any res- 

 ervoir where the air is at atmospheric pressure without losing its 

 potential energy, and hence, if none of its energy is lost, it cannot 

 be used up in heating the air. Is it not like the water in a pond 

 having a certain head or capacity for work f We may enlarge 

 the pond, and allow the water to flow over a larger area; but the 

 capacity for work will be diminished very slightly. X. 



Feb. 23. 



The Balloon Problem. 



The problem of the amount of work done by the gas in a bal- 

 loon expanding as the balloon rises, as proposed in Science for 

 Feb. 19, may be much more significant than even the proposer 

 has thought. Take a bag perfectly flexible and holding two cubic 

 feet. Force out all the air and tie the neck. If we attempt to 

 separate the sides, we shall find it impossible to do so; as 

 the ail- presses upon it fifteen pounds to the square inch. Allow 

 a cubic foot of dry air to enter and again close the bag. We 

 shall find the same difficulty as before in further opening the bag. 

 Consider that the air in the bag has been heated 490°, which will 

 just fill the bag. To separate the molecules has required a work 

 equivalent to lifting 3,160 pounds one foot, and for convenience 

 we say that the gas in expanding has lifted the weight of the at- 

 mosphere. Is it proper, however, to think of the outside air as 

 having been lifted ? Has any more outside air been lifted than 

 the 1.2 ounces that a cubic foot weighs? The work, then, has 

 been internal and not external. This is a very important distinc- 

 tion. The external work has been only that required to lift the 

 weight of air displaced. 



This can be shown best, perhaps, by determining just how much 

 change has taken place in the behavior of the bag to outside in- 

 fluences. If any external work has been done, we ought to be 

 able to measure it. If the bag with its two cubic feel of air were 

 left to itself, it would soar aloft, and it would require a weight of 

 just 1.3 ounces to restrain it. We say the heated air displaces 

 two cubic feet of air at the outside temperature; and since its 

 density is just half that of the outside air, it can lift a weight 

 equal to that of one cubic foot of air. 



Instead of heating the air, let us connect the empty bag with a 

 reservoir having a gas which has a density just half that of the 

 air. Here the conditions are entirely changed. The reservoir, to 

 all intents and purposes, is connected with the outside air, and 

 when we connect the mouth of the bag with it, there is no more 

 work required to expand the bag than if we had opened it into the 

 outside air. In the case before, after closing the bag, we could 

 not open it till some internal work had been done in expanding 

 the air; but now that internal work is not needed, and the only 

 work done by the gas in expanding the bag is that required to lift 

 one cubic foot of air one foot. The lifting power of the bag is 

 precisely the same as it was when it contained air at 490°. The 

 amount of external work in expanding the bag, or capacity to do 

 external work, is exactly the same. 



Take the same bag, empty as at first, and connect it with a 

 reservoir containing two cubic feet of air at the outside tempera- 

 ture but at a pressure of two atmospheres. The air will flow 

 quickly into the bag and an equilibrium will be established with 

 the pressure at one atmosphere in both the reservoir and bag. 

 How much external work has been done? Has the air in expand- 

 ing lifted an enormous weight? Certainly not ; the external work 

 has been equal to that required to lift two cubic feet of air, or 3.4 

 ounces, one foot. Here again we have entirely different condi- 

 tions from those in. the first case. On connecting the hag with 

 the reservoir we virtually opened it to the outside air, and the out- 

 side air did all the work which in the first case was needed to he 

 done in separating the particles of air, or in increasing their 

 kinetic energy. We can see this at once by the following consid- 

 erations. Open the bag into the free air; we can pull the sides 

 apart to their fullest extent. Now connect the opened bag with 

 the reservoir which has the air at the outside pressure, the condi- 

 tions remain exactly as before, when the mouth of the bag was 

 open to the outside air. Empty the bag and connect it with the 

 reservoir. No change will take place, but the reservoir will vir- 

 tually be connected with the outside air. Now gently force air 



