a ee pa a Ee MACHINES: THE THEORY OF THE ACTION OF THE VARI- OUS FORMS OF COLD-PRODUCING OR SO-CALLED ICE MACHINES (MACHINES A FROID). TRANSLATED FROM THE FRENCH OF M. LEDOUX, Ingenicur des Mines, REPRINTED FROM VAN NOSTRAND’S MAGAZINE. NEW YORK: D. VAN NOSTRAND, PUBLISHER, 98 MunnaY AND 97 Wannen Srnzer. 1879. <Callout type="important" title="Important">The theory of Ice-Making Machines has assumed a new importance, since it has been shown that they may be worked to an economical advantage in some sec- tions, even where natural ice is not diffi- cult to be obtained.</Callout> But aside from any question of com- petition with natural ice in temperate climates, the subject is of great interest to those who find it desirable to produce and maintain a low temperature in places where the requisite quantity of ice would be too cumbersome, and where a refrig- erating machine and its driving power can be easily accommodated. Such an example is afforded by the hold of a ves- sel sailing in a warm climate. The conditions of effective working of the three classes of machines are clearly set forth in this little treatise. G. W. P. ICE-MAKING MACHINES.
L Cuarrer L 81. Ir has long been known that air is heated or cooled when compressed or dilated. The mechanical theory of heat defines the conditions under which this heating or cooling is effected, and shows that these effects are proportioned to the ex- ternal work performed by the air, with the restriction that in expanding the resist- ance overcome by the gas is always _ equal to the elastic force of the latter. If ¢ and ¢’ represent successive tempe- ratures of a unit weight of a permanent gas, which has been compressed or dila- ted under conditions above stated in producing an amount of work (either re- sistant or motive) equal to W, we shall have t-'=4w A being the reciprocal of the mechan- ical equivalent of heat =z}; and c being the specific heat of the gas at constant volume. In a saturated vapor a part of the ther- mal equivalent of the external work is transformed into latent heat; the other part alone becomes sensible under the , form of external heat. This is expressed in the fundamental equation —_ ¢,(t—¢') + (ap—2'p’)=AW in which ¢, is the specific heat of the liq- uid, x the proportion of vapor in the unit of weight of mixture of liquid and vapor, p the latent heat of the vapor and W the external work accomplished. ‘We see from these equations that for the same quantity of heat transformed into work, the range of temperatures must be greater with a gas than with saturated vapors.
§ 2. Whether we employ a permanent gas ora vapor, the apparatus designed for the refrigerating effects is based upon the following series of operations: 7 Compress the gas or vapor by means of some external force, then relieve it of its heat so as to diminish its volume; next, cause this compressed gas or vapor to expand so as to produce mechanical work and thus lower its temperature. The absorption of heat at this stage by the gas, in resuming its original condition, constitutes the refrigerating effect of the apparatus. When the cooling takes place at con- stant pressure, the cycle of operations can be represented by the diagram Fig. 1 in which the abscissas represent volumes, and the ordinates pressures.
The gaseous body taken at the press- ure P, and under the volume V, is com- pressed to the tension P, and the volume V,. It is then cooled under constant pressure so that the volume V, becomes V,’, then it is allowed to expand, the pressure P, becoming P, and the volume changing from V,' toV,. Finally it is * brought to the original volume V, by transferring heat to it under constant pressure. The area V,V,V,'V, represents 9 the work expended and the lineV,V, the refrigerating effect obtained. An inspection of the figure shows that a refrigerating machine is a heat engine reversed.
If instead of cooling the gas, to reduce it from the volume V, to V,’, it be heat- ed so as to assume the volume V,’’ greater than V, an amount of work is obtained which is represented by the vertically shaded area V,V,'V,'’V,; the heat expended is represented by the length V,V,”. It should be noticed that in the case of a permanent gas, the changes from volume V’ to V,’ or V,” and from V, or V,’ to V, are accompanied by correspond- ing changes in temperature. In the case of a condensable vapor these changes are effected at a constant temperature, the addition or subtraction of heat taking effect in an evaporation of the liquid or a condensation of the vapor.
§3. From this similayty between heat motors and freezing machines it results that all the equations deduced from the 10 mechanical theory of heat to determine the performance of the first apply equally to the second. If Q, be the quantity of heat taken from or added to a given mass, of com- pressed gas or vapor, and Q the quan- tity of heat necessary to subtract from or add to the expanded mass in order to bring it to its initial state, T, and T, the absolute temperatures correspond- ing to the volumes V, and V, and W the work, either active or resistant devel- oped by the machine. The fundamental principle of the mechanical theory of heat, if the gas returns exactly to its primitive condition, affords the equation, Q,-Q=AW If the cycle of changes is the so-called eycle of Carnot; that is to say, if the lines V,V,, V,’V,, and V,’’V,’ are adiaba- tic curves; then we have Qa @-@ TT, T,—T, The quantity of work developed by a heat motor, under these circumstances, 1 is for each heat unit or calorie, whatever the intermediate agent, W_1T-T, QA T, “The efficiency depends upon the dif- ference between the extremes of temper- ature. . The performance of a refrigerating machine depends upon the ratio between the calories eliminated and the work expended in cooling. It is expressed by a and we have ture of the body employed.
Unlike the heat motors, the freezing machines possess the greatest efficiency when the range of temperatures is small, and when the final temperature is eleva- ~ted. Wz In a freezing machine employing a va- 12 por, T, being the absolute minimum final temperature, this final temperature T, in a machine employing a permanent gas is different from the initial temperature T,, and we have, We can write for the efficiency Q_ T, wrATt_t, Comparing the efficiencies of the two machines it is evident that the perform- ance becomes less in proportion as we obtain lower final temperatures. Theoretically there is no.advantage in employing a gas rather than a vapor in order to produce cold even if the com- pression be made without addition or subtraction of heat. The choice of the intermediate body would be determined by practical consid- erations based on the physical character- istics of the body, such as the greater or less facility for manipulating it; the extreme pressures required for the best effects, etc.
Air offers the double advantage that it is everywhere obtainable, and that we can vary at will the higher pressures in- dependent of the temperature of the refrigerant. But it is cumbersome, and to produce a given useful effect the appa- ratus must be of large dimensions. Liquids on the other hand allow the use of smaller machines, but are obtained only at a greater or less cost. Farthermore the maximum pressure is determined beforehand by the temperature of the refrigerant, and depending on the nature of the volatile liquid; this press- ure is often very high.
§4. The foregoing conclusions are based on the hypothesis that the com- pression and expansion follow the adia- batic lines V,V, and V,’V,, that is to say that the changes of volume and pressure follow the cycle of Carnot. This hypothesis is realized when the cooling is accomplished outside of the compression cylinder and after the gas has been raised to the pressure P,. If the compre: 7 accord- Zs GNIVERSITY CAL PORYEYY 14
§65. The efficiency is calculated in the following manner. ‘We suppose the compression to be made ata constant temperature. Then y Marriotte’s Law we have P,V,=P,V,. The work of resistance to compression would be Vv, Vv, Wr = PV lg RE GG! and we shall have as in the preceding case. AW, =Q, R is a constant, uniform for the air at 29.27 inches and a unit of weight is sup- posed taken. The gas dilating from the temperature T, to T, without gaining or losing heat, we shall have for the work of dilatation, 16 inclusive of the work at full pressure during introduction ; AWn=ke(T,—T,)=Q. The performance is represented by and we have & is the ratio of specific heat at constant pressure to the specific heat at constant volume; this ratio is =1.41 and is the same for all permanent gases. It follows then T,-T, Q a-o-4 (ye Gi oT _1) If the compression follows. an adiabatic curve, we shall have for the efficiency— 17 calling T, the absolute final temperature of the compression It is easy,to show that co T,—T, or ™4@) iG =} is greater than k-1,, ,P, | lp and consequently that the efficiency in the first case is less than in the second. The employment of air presents a cer- tain theoretical advantage over volatile liquids, inasmuch as it admits of cooling toacertain extent during compression.
We will now examine in succession “ gome of the recently invented freezing machines (machines a froid). The Air Machine of M. Giffard; the Sulphurous Acid Machine of M. Pictet, and the Am- monia Machine of M. Carré.
Cuaprer II. x GIFFARD'S AIR MACHINE. § 7. This machine consists of a single-acting cylinder A. the piston of which is furnished with two valves opening from without inward. This cylinder is sur- rounded with a jacket leaving a space within which circulates a current of cold water. There is a second cylinder, B, also single-acting, and having a solid piston, and with a diameter a little smaller than the first. At the bottom of this cylinder are two openings closed by valves, open- ing, one outward and the other inward, and operated by levers which are worked by cams on the driving shaft. The pistons are driven by crank con- nections with the main shaft. The condenser R is a surface condenser and receives a current of cold water from the envelope of the compressor cylinder A. A Reservoir of wrought iron, R’, is connected with the condenser by a tube and communicates also with the bottom of the expansion cylinder B.
§ 8. The air taken in at ordinary press- ure is compressed in the cylinder A till it has the density of that in the reservoir; it is then allowed to flow into the con- denser R and the reservoir R’. During this passage it loses a great part of the sensible heat which it attains during compression, and is brought nearly to the temperature of the surrounding air. During this time the valve s of the cylinder B opens and permits a certain amount of air equal in weight. to that which is expelled from A, to pass from the reservoir into the cylinder producing a certain amount of work. Then the * valve s closes,—the air in the cylinder B expands producing again work which may be deducted from the work of compression and the temperature is lowered. When the piston B reaches the upper limit of its stroke, the valve s’ opens and the cooled air as the piston descends escapes by the tube T.
The cooling experienced by the air, during compression, by contact with the cooled sides of the cylinder is scarcely sensible. 21 The machine therefore acts under con- ditions set forth in § 2 and we know that its useful effect cannot exceed the value By means of the adjustable cams we can regulate at will the action of the valves sand s’. If we shorten the time of admission into the cylinder B, the pressure will increase in the reservoir; for the amount flowing into B should be equal to that forced into the reservoir from A. The temperature of the air ex- pelled will then be less. If, on the con- trary, we increase the time of admission the reservoir pressure will diminish, .and the temperature of outflowing air will be increased. The apparatus presents: then this im- portant peculiarity—that we can vary the useful effect of the machine at will, through wide limits.
As the air leaves B, at the pressure of the atmosphere, the minimum limit of pressure is established, below which the 22 expansion cannot be pushed, and which is controlled by the relative dimensions of the two cylinders. We will proceed to calculate the cool- ing effect produced by this machine and the corresponding work required.
We shall neglect at first the effect of waste spaces in the machine, and of watery vapor in the air.
§ 9. Let P,, t, and T, be the pressure and temperature (counted from absolute zero) of the air. V, the volume described by the piston A. V, the volume of air when at pressure P,. V, is then the volume described by the piston during the out- flow. m=weight of air whose volume passes from V, to V,. P,,t, and T, the pressure and temperature of compressed air delivered from A. V,’t,/ and T,’ the volume and 23 temperature after passing into the condenser. V, the total volume described by piston B. P,, t, and T, the pressure and temperature of the air at the end of the course of this piston.
During compression the cooling by simple contact with the sides of the cylin- der is insignificant. We shall neglect this and also assume that no heat is receiy- ~ ed from the sides of the cylinder B.
FIRST PERIOD: COMPRESSION.
§ 10. When air is compressed without losing or gaining heat, the pressure and temperature at each instant bear the re- lation to each other expressed by the equation PL = P,V! @) in which & is the ratio of specific heat of constant pressure to the specific heat of constant volume. 0.28751 =e tt
Gay Lussac’s law affords, P,V,=RmT, (2) and P,V,=RmT, (3) From equations 1 2 and 3 we deduce kt eI The work of the resistance to compression and outflow is k Wr = gaa PV. -P.Y)- (6) We have elsewhere he es k—-1~AR c being the specific heat of air of con- stant volume. Equation (6) then becomes mke = (1-7). 0)
SECOND PERIOD: COOLING. The air is cooled in the condenser under constant pressure. |The volume W, 25 changes from V, to V,’, and the temper- ature from ¢, to ¢,'. Ca we have; V/=Vr (8) and the quantity of heat imparted to the water of the condenser is; Q,=mke(T,—T,’) (9) If T,’=T, then R,=AW, os THIRD PERIOD; EXPANSION. The volume V,’ of air enters the cylin- der B yielding an amount of work equal toP,V,’. It expands from V,' to V, with- . out gain or loss of heat. We have then: . P,V#=P,Vs, (10) PV, SRmT,’, (id) P,V,;=RmT, (12) BA whence T,=T/(E:) * (13) : @) The work performed by the air is k Wn= Rae, ’—P,V,) (14) Ke * Wa= 7 (1-1) (15) The resistances to be overcome by exter- nal force amount to W.-W (0,1) (2,-7.6) If the machine works properly, the final pressure P, should be equal to the at- mospheric pressure. The equations (10) (12) and (18) give Yow Wry, : 17 or v,_T (17) v,~ Tt Tf and rat (18) Equation (17) expresses the ratio which should exist between the volumes of the two cylinders, in order that theair be finally expelled at atmospheric pressure, after having been compressed by a force P,.
The negative heat (cooling), produced by the apparatus, is the quantity of heat necessary to restore the air from the temperature ¢, to the temperature ¢,, under constant pressure. 27 Q=mke(T,—T,) Q=mber,(1 -7) } a9)
§11. Since a given weight of air is re stored, at the end of the operation, to the same temperature and pressure it had at the beginning it follows, that it has been through a perfect cycle. <Callout type="tip" title="Tip">The Giffard machine can be adjusted for varying levels of cooling effect by altering the time air spends in the compression cylinder B.</Callout>
<Callout type="warning" title="Warning">Be cautious when operating the machine as it requires precise adjustments to avoid overheating and potential damage.</Callout>
Key Takeaways
- The Giffard air machine can be adjusted for varying levels of cooling effect by altering the time air spends in the compression cylinder B.
- Air offers a theoretical advantage over volatile liquids as it allows for some cooling during compression.
- The efficiency of refrigeration machines depends on the range of temperatures and the final temperature achieved.
Practical Tips
- Adjust the Giffard machine's operation by varying the time air spends in the compression cylinder B to achieve desired cooling levels.
- Utilize air as a refrigerant when space is limited, though it requires larger apparatus compared to liquids.
- Understand that the efficiency of refrigeration machines improves with smaller temperature ranges and higher final temperatures.
Warnings & Risks
- Be cautious when operating Giffard's machine as precise adjustments are required to avoid overheating and potential damage.
- Air compression can be cumbersome, making it less practical for portable or small-scale applications compared to liquids.
- The theoretical advantage of air over volatile liquids in cooling during compression is limited by the need for larger apparatus.
Modern Application
While Giffard's air machine may seem outdated, understanding its principles and limitations can provide valuable insights into early refrigeration techniques. Modern refrigerators have vastly improved efficiency and compactness but still rely on similar thermodynamic principles. This knowledge remains relevant in historical research and the development of sustainable cooling technologies.
Frequently Asked Questions
Q: How does Giffard's air machine work?
Giffard’s air machine operates by compressing air, allowing it to cool as it passes through a condenser before expanding and producing mechanical work. The process can be adjusted for varying levels of cooling effect.
Q: What is the theoretical advantage of using air in refrigeration machines?
Air offers a theoretical advantage because it allows some cooling during compression, which is not possible with volatile liquids that require higher pressures and temperatures.