then been taken from the steam without reducing its temperature till the whole had condensed, the drop of entropy would be represented by AG (or ag), and the quantity of heat abstracted by the area aAGg. This last quantity is obviously

the latent heat of steam at the ratio of the area aAEd to the area aAGg is the fraction of the latent heat available to be given up after the steam has expanded, according to the line DE. This ratio must therefore represent the fraction of the steam uncondensed at E. The areas

100° F., and it is evident that

are proportional to the lines AE and AG, and therefore

AE AG

represents the dryness fraction, or the fraction of the steam uncondensed after the adiabatic expansion DE has taken place, or when the point E is reached during the isothermal withdrawal of heat GA. Similarly, if any other horizontal line

such as HKL be drawn,

HK
HL

may

will represent the dryness fraction.

of the steam at the point K of the adiabatic expansion DE. The curve DG may be drawn by obtaining from a table the entropy of dry, saturated steam at several temperatures, or it be obtained in another manner. AG × Aa = area aAGg. But a A represents a certain temperature, and aAGg represents the latent heat of steam at that temperature. Therefore the length of AG can be obtained by dividing the latent heat by the temperature. Several horizontal lines, such as AG and HL, can thus be determined, and the curve DLG drawn through

their ends.

CHAPTER VII.

THEORETICAL CONSIDERATION OF DIFFERENT TREATMENTS OF

STEAM IN A HEAT-ENGINE.

It is intended in this chapter to consider the effects of treating steam in different ways on the efficiencies of heat-engines with special reference to the steam turbine.

Let us consider the transfer of heat energy into mechanical energy in a heat-engine or apparatus comprising a boiler in which water is heated to a certain temperature and then converted into steam, a turbine or other motor in which the steam is expanded and loses some of its heat, and a condenser in which more of the heat is taken from the fluid before the latter is returned to the boiler.

The different cases which will be considered have been chosen not to represent what occurs in practice, but to indicate the effects of different treatments of the steam, so that it can be ascertained what had best be done with any type of turbine, in order to prevent waste and promote efficiency, and what is likely to be gained or lost by any alteration in treatment, such, for example, as by superheating the steam.

CASE I.

Let us suppose, in the first instance, that feed water is received into a boiler at 85° F., and heated to 382° F. The

entropy-temperature curve for this heating is shown at AB, in Fig. 84.

Suppose that the water is converted into steam at this temperature, which means that the pressure is 200 lbs. absolute.

This absorption of heat is represented by BC. Let the steam now expand adiabatically, doing work, till the pressure falls to 0.6 lb. absolute. The temperature corresponding to this pressure is 85° F. This expansion is represented by the line CD on the diagram. Some of the steam will condense during

FIG. 84.-Case I.: Adiabatic Expansion; iso

this expansion, and we can

thermal compression; range of tem- find the wetness at any perature, 85° F.-382° F.

point in CD, by the method described in connection with Fig. 83. Lastly, let heat be abstracted from the fluid till the whole of the steam has condensed, but without any reduction of temperature, and let the water be returned to the boiler. This action is represented by DA on the diagram (Fig. 84). It does not matter whether the heat be abstracted from the steam in the turbine or in a condenser, or in any other vessel, provided that it takes place after the expansion and the fall in temperature are completed.

The heat supplied to the fluid is then represented by the area a ABCd, and the heat abstracted by the area aADd. The heat converted into work is therefore represented by the area ABCD and

Let us suppose now that the steam generated at 200 lbs. pressure, instead of expanding adiabatically, be supplied during expansion with suffi

cient heat to prevent any condensation.

This might be approximately attained by jacketing a steam turbine with hightemperature steam. The condensation will then all take place at constant temperature, as shown by EA. The entropy temperature diagram will then be as shown in Fig. 85.

382

FIG. 85.-Case II.: Expansion along Line of Dry Saturated Steam; isothermal compression; range of temperature, 85° F.-382° F.

The heat supplied to the fluid is represented by the area a ABCEe, and the heat abstracted by the area aAEe. The heat converted into work is therefore represented by the area ABCE, and

Compared with Case I. it will be seen that there is an increase both in the heat supplied and in that converted into work, but the latter is not increased proportionately to the former, and hence the drop in the efficiency.

1

CASE III.

Suppose in this case that the steam, instead of receiving heat while expanding, has heat taken from it, as, for example, by radiation from the exterior of a turbine.

FIG. 86.-Case III.: Expansion with Leakage of

Suppose that by this

means twice as much steam is condensed during expansion as in Case I. The entropytemperature diagram will then be as shown

heat; isothermal compression; range of steam is condensed temperature, 85° F. — 382° F.

at constant tempera

ture, as shown by the line FA. The heat supplied to the fluid is represented by the area aABCd, and the heat withdrawn by the area a AFCd. The heat converted into work is therefore represented by the area ABCF, and—

The heat supplied is the same as in Case I., but the portion of this that is converted into work is less than in Case I. by the amount represented by the triangle CFD. The efficiency is therefore less than in Case I.

The total leakage of heat during expansion is represented