April 30, 1903] 



NA TURE 



60 ' 



presents the work done in any small or large change 

 of state. Since d\\ = t.d<p, the area of a t,<p diagram 

 represents the heat received. If students have the use 

 of two blackboards on .which they can, without trouble, 

 show bv the coordinates of a point the p and v or the 

 t and of a pound of stuff, the whole thermodynamic 

 conditions are known. If the state of a pound of any 

 kind of stuff is given in any way, it is good to be able 

 quickly to show it by a point either on the p,v or on the 

 /,<p diagram. Therefore these blackboards have equi- 

 pressure and equi-volume curves permanently marked 

 upon them. Thus on a water stuff blackboard a student 

 can mark in chalk, without any trouble, such points 

 as these : — 



(1) A pound of water steam, So per cent, water, 10 

 per cent, steam at a pressure of 80 lb. per square 

 inch. 



(2) A pound of water steam at So lb. per square inch, 

 its volume being 3 cubic feet (the volume of the part 

 which is water is neglected). 



Or he can quickly work such exercises as these : — 



(3) The stuff of (2) is cooled at constant volume to 

 30 lb. per square inch, show how it changes its state; 

 find the heat abstracted. 



(4) The stuff of (2) is expanded adiabatically, make 

 a table showing its p and v at every instant and draw 

 .1 />,;• diagram showing the adiabatic expansion. State 

 the dryness of the stuff at each point. 



But why go on? It is evident that with such a 

 board, with chalk and a sponge an experimenter can 

 work the most interesting problems. He sees at once 

 the thermodynamic inefficiency when heat is given to 

 boiler feed water ; the small thermodynamic efficiency 

 of superheating; the wetting effect of expansion of 

 dry steam ; the drying effect of expansion on very wet 

 steam ; the heat given and the work done in any change 

 of state. 



We have found that this practice with blackboards 

 leads to the most exact quantitative and practical know- 

 ledge of what goes on in heat engines. But the student 

 must really state the answers as to heat and work 

 exactly, the scales to which energies are represented 

 being familiarly known. After a little practice, the 

 ghostly quantity entropy gets to be as well known as 

 electrical potential now is to experimenters — in 1868 

 it was merely a mathematical expression to most 

 students, just as entropy now must remain to anybody 

 who will not experiment. 



An indicator diagram shows the pressure and the 

 travel of the piston, and therefore we may say, the 

 volume displaced behind the piston, but we do not call 

 it a p,v diagram. Its value in enabling the indicated 

 horse-power to be calculated, in telling how the valves 

 and passages perform their duties, is, as we know, 

 very great. But when we desire to use it in our study 

 of the thermodynamics of the engine, we must first 

 endeavour from our other measurements to find out 

 how much stuff, water-steam or air or other gaseous 

 mixture, is undergoing the changes of pressure and 

 volume which are recorded. We must also know the 

 actual volume of the stuff at every instant, and we get 

 this by adding the volume of the clearance. We can 

 now draw a p,v diagram, but it is not sufficiently 

 NO. ) 748, VOL. bj] 



noticed by students that it is only on certain assump- 

 tions being made that we can study the p,v diagram 

 for a whole cycle of operations. For example, in a gas 

 engine cylinder, we can draw the p,v diagram from 

 the beginning of the compression, through the ignition 

 and expansion parts until the exhaust valve opens, on 

 the assumption that there has been no leakage past 

 valves or piston. The p,v diagram of all the rest of 

 the evele is drawn on the assumption that something 

 which is really occurring elsewhere is occurring in the 

 cylinder itself. We consider that in the hands ot 

 elementary students the assumed p,v diagram for all 

 other parts of the cycle may be very misleading. Un- 

 fortunately, it is seldom that one finds an author who 

 is careful to explain these assumptions, which, when 

 clearly understood, do enable most valuable calcula- 

 tions to be made. The idea underlying a p,v dia- 

 gram is that any point shows the p and v of a certain 

 quantity, say a pound, of the stuff. That is, it is all 

 at a certain p. But during release, part of it is at one 

 p and part at another, and during release, therefore, to 

 speak of a p,v diagram is absurd. The assumption 

 on which we usually proceed is that we shall let the 

 area of what we call our p,v diagram represent the 

 work done upon the actual piston. 



Again, in a steam engine cylinder we can draw the 

 real p.v diagram from cut off to release. All the rest 

 1 hi' cycle is drawn on the above assumption as to 

 work. In drawing the /,<p diagram we assume that the 

 stuff is all at the same temperature at any instant and 

 every point on this diagram corresponds without am- 

 biguity with a point on the p,v diagram, but it is on 

 the assumption that we do actually know the weight 

 of stuff we are dealing with. Given any p,v diagram 

 for a given quantity of any kind of stuff, one, and only 

 one, /,<£ diagram can be drawn. The p,v diagram, 

 shows by its area the work done in every change, the 

 other shows the heat given to the stuff in every change ; 

 the net area of any closed part of the one is equal to 

 the net area (taking the same units for heat and work) 

 of the corresponding closed part of the other. 



It will be found that every engineer who has pub- 

 lished speculations based on such diagrams has really 

 kept in his recollection the assumptions on which they 

 are drawn, but it seems a pity that for the sake of 

 elementarv students they should not specifically discuss 

 these assumptions. 



In refrigerating machines, in gas arid oil engines, 

 there is probably greater equality of temperature 

 throughout the mass of stuff at each instant than there 

 is in the water-steam of a steam engine cylinder. The 

 state of things inside a steam engine cylinder is verj 

 complex on this account, but the p,v and /,$ diagrams, 

 although based upon simple assumptions, really do 

 lead us a long way in our study of what happens. 



All engineering calculation is based on simple 

 assumptions; the engineer knows that real problems 

 are very much more complicated than any such assump- 

 tions suggest, and that experience and wisdom are 

 needed by all men who are going to make use of such 

 calculations. There are foolish men and foolish books 

 which give students the notion that the simple assump- 

 tion represents truly the real case, but the true en- 



