Energy.—When steam is formed (starting, say, from the state of water at o° C) heat is taken in, and some external work is done by the expansion of the substance. The difference, which depends simply on the final state and not on the manner of formation, is called the internal energy E.
The total heat I is conveniently defined by the equation I = Ed-APV , where P and V are respectively the pressure and volume of the substance, and A is a factor which converts units of work into units of heat. Hence when the substance is heated under con stant pressure the change of I is measured by the quantity of heat that is taken in, for it is then equal to the gain of internal energy plus the work done. In a process of throttling it is easy to show that I does not change, provided there is no loss of heat to other bodies.
To define entropy, it may be said that when the substance takes in heat in a reversible manner (namely a manner which excludes the existence of any turbulent movement) its entropy changes by the amount
where Q is the heat taken in and T is the temperature (on the absolute scale) at which it is taken in. If T is itself changing while the heat is being taken in, we must write this change of entropy as f
• Thus when steam is formed in a quietly steaming boiler, at a constant temperature T, from water at the same temperature, the entropy 4 changes by the quantity
where L is the "latent heat." Like the other quan tities, the entropy of water at o° C is reckoned as zero for con venience in tabulation. Both the entropy of steam and the total heat are quantities of great importance in the theory of the steam engine (q.v.).
Imagine a quantity of superheated steam at any usual temperature to be compressed while the tern perature is kept constant. When the pressure reaches a certain value condensation begins, and we are then dealing with a sub stance which is partly water and partly saturated steam. The pres sure in question is that which corresponds to saturation at the assumed constant temperature. This pressure will not rise further until all is condensed: after that the pressure on the water may of course be increased to any extent. The process is discontinuous, with three distinct stages. Suppose this experiment to be re peated at various temperatures : it will be found that when the temperature is sufficiently high there is no stage during which both water and steam are present together. When this tempera ture is reached or exceeded, the substance passes, as its pressure is increased, from the condition of steam to that of water—from vapour to liquid—in a continuous manner without ever being a mixture of the two. The lowest temperature at which this can happen is called the critical Temperature, and the limit of pressure above which the substance cannot exist as a non-homo geneous mixture of liquid and vapour is called the critical Pres sure. These conditions of pressure and temperature constitute
the "critical point." The critical temperature of steam is about
C and the critical pressure about 3,158 lb. per square inch.
The properties of steam in the neighbourhood of the critical point are less exactly known than at lower and more usual pres sures. The "characteristic equation" on which Callendar founds many of his tabulated values applies with sufficient exactness within the lower range of pressures commonly met with in engi neering practice. It takes the form where V is the volume (per lb.), T is the absolute temperature, P is the pressure, R is a constant relating to the ideal volume of a "perfect" gas, b is a constant which expresses the additional volume of the molecules, and c is a term, depending on the temperature, which expresses the loss of volume through "coag gregation" or temporary association of molecules. The equation is applicable to the superheated as well as the saturated state.
When steam is cooled to a temperature at which condensation should occur, it is found, when no nuclei are present about which water droplets may form, that the temperature may fall some way below the temperature of satu ration bef ore condensation begins. A temporary and unstable state may accordingly be produced, called super-saturation. The vapour in this condition may be described as supercooled : its state is analogous to that of a liquid cooled below its melting point with out crystallization.
Air.—Water vapour is one of the constitu ents of the atmosphere, the proportion depending not only on the temperature but on other causes which affect local dryness. At any given temperature air is said to be saturated with water vapour when the proportion present is such as to exert a partial pressure equal to the pressure of saturation corresponding to the given temperature. Any excess tends to be thrown out as mist or rain : any less quantity than that required for saturation is held as an invisible constituent, namely, in the state of super heated steam. The quantity of water-vapour present in air may be expressed as a fraction of the quantity which would cause saturation : this fraction is called the "relative humidity" of the air. The "dew-point" is the temperature to which air must be cooled to allow a deposit of water to take place.
Air is often dried for industrial uses by cooling it to a very low temperature. This causes it to deposit nearly all its contained moisture, which is then drained away, leaving only the trifling quantity that suffices to produce saturation at the low tempera ture. When the air returns to normal temperature without taking up more water its relative humidity is very small.
See Regnault, in Mem. Inst. France (1847, Vol. XXI.) ; H. L. Callen dar, Properties of Steam (1920), and The Callendar Steam Tables (1915) ; J. A. Ewing, Thermodynamics for Engineers (1920).