To many it will be a matter of indifference how the results are reached, provided only that they are reached correctly and swiftly. To these it may be said that entropy is a mathematical quantity depending upon heat and temperature, such that, when any thermal operation is plotted with temperature for abscissae and entropy for ordinates, the mechanical work involved is represented by the area included, precisely as it is with coordinates of pressure and volume in the ordinary indicator-diagram. This quantity has been determined for 75 lbs. of dry air, for the vapor contained in it, and for the sum of these, exactly as for the corresponding quantities of heat, and these are plotted on the upper side of the same temperature axis as the latter. These curves are numbered respectively IV, V and VI.

The theoretical or perfect cycle of operations of the ammonia-compression machine is represented on this diagram by a rectangle whose right-hand end is the ordinate at the condensing temperature of the ammonia. Its top is a horizontal line at a height determined by the total entropy of the air to be refrigerated, and its bottom is one at a height determined by the entropy after refrigeration. (These will be called hereafter the lines of maximum and minimum entropy respectively.) Its left-hand end is determined by the suction or absorption temperature of the ammonia, which must be low enough to absorb heat from the air at the lowest temperature to which the latter is to be reduced. In practice the suction temperature is never less than 10° F. lower than this; and similarly the compression or condenser temperature is never less than 10° higher than that of the condensing water.

Under normal conditions cooling-water at 70° F. to 75° F. will always be available for condensing purposes in hot weather, and the maximum condenser temperature used in these diagrams is accordingly 85° F.; also, in all the cases taken for analysis in this article, this is the condenser temperature assumed, unless otherwise stated.

If we assume a uniform difference of temperature of 10° on the two sides of the expansion coils, we might construct a curve lying uniformly 10° F. to the left of the total entropy curve, that is, having a temperature 10° F. lower for the same ordinate in each case, and the lower left-hand corner of every rectangle would lie on this line, thus determining the rectangle completely, as the top and bottom lines are in all cases the lines of maximum and minimum entropy, and the right-hand end is the condenser temperature as before, the left-hand end being then determined by the intersection of the line of minimum entropy with the proposed curve. This curve, however, is not drawn on Fig. 242 for the reason that the area of the rectangle so determined would have to be multiplied by R, which would have to be determined from the absorption and condenser temperature in each case, in order to give the actual power required.

In order to avoid this necessity three auxiliary curves are plotted in dotted lines, which give the actual power requirements direct, with an assumed temperature difference in all cases of 10° F. at the refrigerating coils, and for three different condenser temperatures, respectively 85° F., 70° F., and 55° F., corresponding to the temperature of cooling-water available under different conditions and at different seasons.

The simple rule for the use of these curves is: Draw the lines of maximum and minimum entropy, both extending to the proper condenser temperature on the right, and the latter extending to the left to its intersection with the corresponding dotted curve; at this point erect the vertical which completes the rectangle. The area of this rectangle in square inches gives the horse-power required per 75 lbs. of air for refrigeration between the limits chosen.

At various heights on the diagram the difference in temperature between the entropy curve and the assumed condenser temperature is taken, increased by 10° F., and the sum multiplied by R as determined from T1-T2/T1 for that point. This product is not in any way to be considered as a temperature, but only as a length, and is set off to the left of the condenser temperature used, with the ordinate for which the temperature difference was taken.

These points are connected by the dotted curves, and when the left end of the rectangle is drawn upward from the intersection of lines of minimum entropy with the appropriate curve, its right end and top being, as before, the condenser temperature chosen and the line of maximum entropy, it is evident that the length (and therefore the area) of the rectangle has been increased in the ratio R, thus giving actual horse-power.

In using these curves care must be taken to use the one corresponding to the condenser pressure in the given case. If this be different from any of those given, the curve corresponding can be interpolated by eye with all the accuracy necessary for most purposes.

It must also be noted that the curves are only correct for the "direct expansion" system, that is to say, where the ammonia is expanded in the coils over which the air passes.

In the brine-circulation system the ammonia is expanded in coils immersed in a tank of brine, which is afterwards circulated through coils in the refrigeration chamber. It is obvious that this system requires twice the expense for coils or pipe surface, and also requires twice the temperature-interval between the temperature of the expanding ammonia and that of the air, required by the direct-expansion system, since the heat requires to be transmitted through the walls of two sets of pipes instead of one. It is for the latter reason that the curves given are not correct for the brine system. To make them correct for this case at least 20° F. should be added, instead of 10° F., to the difference of temperature between the points on the entropy curve and the condenser temperature. This of course would give a new value of T1-T2/T1 and a new and larger value of R to correspond, so that the length of the rectangle for this case would be very materially augmented.