34 



THE POPULAR SCIENCE MONTHLY. 



the vacuum, or separate the gases preparatory to diffusion, requires an 

 expenditure of energy at least equal to the mechanical effect to he 

 derived. 



Since the reversible engine is as efficient as any heat-engine, and 

 since all reversible engines of whatever construction and whatever the 

 working substance have the same efficiency, it is allowable, in dis- 

 cussing the question as to the amount of mechanical effect derivable 

 under given conditions from a given amount of heat, to assume any 

 form of reversible engine, using any working substance which may be 

 most convenient. And it makes no difference whether the engine 

 assumed be practically possible, so long as we know the properties of 

 the working substance well enough to determine its action under the 

 assumed conditions. Sir W. Thomson, before 1851, assuming Car- 

 not's engine with air as the working substance, furnished us with a 

 very complete discussion of this question. The properties of air in 

 relation to heat are very simple. Heat expands and cold contracts it 

 with great uniformity. Compression heats and expansion cools it ac- 

 cording to a well-known law. The effects of any change of volume or 

 of temperature in the cylinder of an engine can, therefore, be exactly 

 predicted. 



Suppose a given mass of air to be compressed and the heat devel- 

 oped by compression removed, so that its temperature remains con- 

 stant. The pressure exerted by it will increase, as shown graphically 

 in the annexed diagram, where a, measured on the horizontal axis 



x, represents the initial 

 volume, and a e perpen- 

 dicular to O x represents 

 the pressure exerted at that 

 volume. Ob, c, and 

 d, represent other volumes, 

 and bf, c g, d h, the corre- 

 sponding pressures. The 

 >< curved line e f g h, drawn 

 through the extremities of 

 the perpendiculars, repre- 

 sents to the eye the relation between volume and pressure when tem- 

 perature is constant. It is called an isothermal line. Now, suppose 

 the air to be compressed without loss or gain of heat. It is warmed 

 by compression, and the rise of temperature causes it to exert a greater 

 pressure. If, then, the substance be at the same initial volume, pres- 

 sure, and temperature as before, and it be compressed to the volume O 

 b without loss of heat, the pressure exerted will be b m greater than 

 b f. Similarly the pressure c n will correspond to the volume c, 

 and d o to d. The line I m n o, which shows the relation between 

 volume and pressure when no heat enters nor escapes, is called an 

 adiabatic line. 



Fig. 1. 



