2 another pressure p2, this difference of pressure being P2, maintained by the continued action of the compressor. The condenser is kept cool with water, and by the time the refrigerant reaches the position 1, it may be supposed that it will have come to the same temperature. Its state will there be defined by the three quantities p1 (pressure in atmospheres), T1 (absolute temperature on the Fahrenheit scale), and v1 (the volume in cubic foot of 1 lb. weight): it is always in the liquid form at this stage. In passing through the expansion valve the temperature always falls, and part of the liquid usually evaporates; hence in the position 2 the state is given by P2, T2, and V2 where P2 and T2 are each less than p1 and T1, while v2 is greater than v1; V2 v, is, of course, the volume of 1 lb. of mixed liquid and vapour in the proportion in which they exist at this stage. (As has been explained, this position must not be taken so near the throttle as to be affected by the rapids which exist there; neither should it be taken so far away from it that heat may have had opportunity of being received through the refrigerator walls; for it is supposed that the change from 1 to 2 is taking place without any access of heat.) While flowing through the refrigerator it is receiving heat, and more liquid evaporates in proportion; the state at position 3 will be denoted by p, T, v1⁄2, and it is supposed to be still sensibly in this state when sucked into the compressor. The compression which ensues is supposed to take place adiabatically; the result is that the temperature and pressure are much higher at 4 than at 3, while the specific volume is less: these will be denoted by T1 P4 4 Ꭲ 4' The changes of entropy that correspond can be obtained from the general chart if the values of the temperatures T1 and T, and the pressures p1 and p, are given. Con 2 siderable modification can be made in practice by adjustment of the expansion valve, and hence several cases arise. The chief variation is in the amount of liquid present in the vapour in position 3. If it is all evaporated here it will be superheated at the end of the adiabatic compression (dry compression); any amount of liquid may be allowed to remain (corresponding to the priming in a steam-engine) by adjusting the expansion valve, and these give corresponding degrees of "wetness" in compression (wet compression). All the inferences are obtained by measuring the diagrams. Carbonic Acid Machines will be first considered. = Carbonic Acid Machines working without Superheating and with Expansion Cylinder. The case taken first is one in which the temperatures at 1 and 2 are 70° F. and 5° F. respectively. Their corresponding absolute values will be T1=530 and T, 465. The saturation pressures at these temperatures are 60 and 24 atmospheres approximately. If the vapour never superheats and is all just condensed into liquid when it reaches the expansion valve, the reversible cycle (which is taken as the standard) is the cycle ABCD, fig. 14. The fraction of liquid unevaporated at A (position 3) is AF EF lb. (since the change of entropy is proportional to the mass evaporated, and the whole mass whose circulation is being followed is 1 lb.)--i.e., about 23 lb. and after the adiabatic expansion CD, the amount ED lb. 31 lb. is already in the state of vapour. Con EF sequently the amount left for producing useful refrigeration is (1-23-31) lb. =46 lb. The heat it removes is change of entropy x absolute temperature area lying between DA and the base line drawn through the absolute zero of temperature—i.e., 53 B.T.U. ABCD Work done by compressor = area ABCD = 7·41 The coefficient of performance 53 = =7·15, 7:41 as it should be). 2 Carbonic Acid Machines working without Superheating and with Expansion Valve. If an expansion valve is employed, the expansion will terminate at some point H instead of D, and its position may be determined by means of a p.v. diagram. [It is in practice taken such that DHX T-area EDC on the entropy diagram; it can be shown that this always gives too low a value, and in many cases much too low. In this particular example the area EDC 2.62 thermal units, while the heat represented by DH (calculated by the exact rule) is 4.60 thermal units 1i.e., roughly, twice as great.] Instead of 530 units available for refrigeration, there are now only 530-4-60=48-40 units. The work to be done by the compressor is increased by an equal amount-i.e., it equals = 7.41+46012-01 thermal units, and the coefficient of performance is reduced to 48.40 1 In the case of CO2 the following approximate rule for calculating this is very nearly exact:-Add difference of pressure in atmospheres to the area ECD expressed in thermal units; the sum is the quantity of heat represented by DH. If the condenser temperature is above 70° F., this rule gives rather too low a value. In measuring quantities of heat by means of areas on an entropy diagram, it must be borne in mind that the area in square centimetres (obtained by adding the number of squares on millimetre paper or by a planimeter) must be multiplied by the physical equivalent of 1 sq. cm.; thus, if a horizontal centimetre represents '02 unit of entropy, and one centimetre height represents 10° F., the physical equivalent of 1 sq. cm. is 02 × 10=2 British thermal unit. The geometrical area must be multiplied by 2 in order to yield the result in B.T.U. Again, in a p.v. diagram it must be remembered that if p is in lbs. per square foot and v in cubic feet, the areas, when reduced as above, express work in foot-lbs; to obtain it in thermal units one must further divide by 778 the mechanical equivalent of heat, which is less than two-thirds the maximum possible. Each lb. of material circulating also removes less heat, which is an additional defect as we have previously indicated. Carbonic Acid Machines working with Superheating.— Now take a case in which the liquid is just all evaporated in position 3. The corresponding position on the entropy diagram is F; it is then adiabatically compressed till the pressure is p1-i.e., it will pass along the vertical FG till it reaches the continuation backwards of the constant pressure line CB at G. Its temperature is seen (by diagram) to rise to 130° F., and at this temperature it enters the condenser, which is at 70° F. It consequently at once begins to part with its heat to the walls of the condenser, and thus a second irreversible stage is introduced-i.e., a stage involving unnecessary performance of work. (In fact, if the adiabatic compression had ceased at J and then the vapour were compressed isothermally to B and thence to C, the reversibility would be restored and less work performed by the amount BGJ; the last portion of the compression JG is wasted, producing a deleterious rise of temperature, and the heat tumbles tumultuously out without doing its full share of work, when it gets into the condenser which is at a much lower temperature. This may be otherwise expressed by saying that we restore availability by doing external work upon the substance along JG, and then we wilfully let it fritter itself away while falling in temperature.) By allowing the whole liquid to evaporate in the refrigerator, the additional refrigerating effect, AF x abs. temp. 26.04, is gained in each cycle, but the compressor has to do greater additional work, viz., ABGF=5.20. With superheating then = |