28 Prof. TyndalPs Notes on Scientific History. 



behaves like the air under constant pressure. The heat neces- 

 sary to the expansion of the steam is X-f-Y. When the steam 

 is cooled, the pressure of the piston is absent, or it is exercised 

 in a greatly diminished degree : hence, in cooling, the heat 

 given out will be X. With every stroke of the piston, there- 

 fore, there is the loss of heat Y ; that is to say, with the action 

 of the engine a consumption of heat is inseparably connected. 



8. From the quantity of fuel consumed in an engine, the 

 total expenditure of heat may be calculated. The loss by radia- 

 tion, transmission, and convection being subtracted, the re- 

 mainder is the usefully applied heat. As, however, by far the 

 greater part of the unused heat can be but roughly estimated, 

 only an approximate result can be thus obtained. More sharply 

 and more simply the problem may be solved by calculating the 

 quantity of heat rendered latent when a gas expands under pres- 

 sure. Let the amount required to heat a gas at constant volume 

 l°bea7; to produce the same elevation of temperature under 

 constant pressure the heat necessary will be x + y. Let the 

 weight raised in the latter case be P, and the height to which it 

 is raised h ; then we have 



y=Vxh. 



A cubic centimetre of atmospheric air at 0° and 76 millims. 

 barometric pressure weighs 0*0013 of a gramme; warmed 1° 

 under constant pressure, it expands 2^4^ °f ^ s volume, and 

 lifts a mercury column 76 centimetres long and of a square cen- 

 timetre basis to a height of 274 tn °f a centimetre. 



The weight of this column is 1033 grammes; the specific 

 heat of air, according to De la Roche and Berard, is 0*267 ; 

 hence the heat communicated to our cubic centimetre of air in 

 order to raise its temperature 1° is equal to that which would 

 raise the temperature of 0*0013 x 0*267 = 0-000347 of a gramme 

 of water 1°. 



According to Dulong, the specific heat at constant pressure is 

 to that at constant volume as 1*421 : 1 ; therefore the quantity 

 required to raise the temperature of our cubic centimetre of air 

 at constant volume 1° would be sufficient to heat 



^i 7 = o-ooo 2 4 4 



l*4<£l 



of a gramme of water 1°. 



Hence the difference {pc + y)— x } or 



y=0-000347-0-000244=0-000103 

 thermal units, by which a weight P=1033 grammes is raised to 



