10 HEAT. 



in heat from the source, converts some of it to work, and gives out the 

 balance to the receiver. When the engine is imagined to work under 

 certain ideal conditions first prescribed by Carnot (whence it is known 

 as a Carnot engine), the fraction of the heat received which is converted 

 into work depends solely on the temperatures of the source and receiver, 

 and for two given temperatures is the same whatever working substance 

 is used. Or, putting the statement in another way, the ratio of the heat 

 put in at the higher temperature to the heat put out at the lower 

 temperature depends solely on these temperatures. We may therefore 

 use the Carnot engine to give us a scale of temperature in the following 

 way. Let a quantity of heat Q l be put in at the higher temperature which 

 we will denote by O l and let a quantity Q 2 be put out at the lower 

 temperature 2 . Then we fix the ratio of these temperatures by 

 putting 



If we keep l and Q l constant, Q 2 is less the lower # 2 . If all the 

 heat Qj is turned into work, none remains to be put out at 2 . In this 

 case Q 2 is zero and therefore 2 is zero. This implies that the new scale 

 dates from a point such that a Carnot engine working down to that 

 point will turn all the heat which it receives from the source into work. 

 We can imagine no greater degree of cold than that of such a receiver, 

 and its temperature is therefore termed the absolute zero. 



It can be shown that if a Carnot engine works between the tempera- 

 tures of boiling water as source, and melting ice as receiver, then for 

 every 373 parts of heat put in at 100 C. it will turn out about 273 parts 

 at C. and convert 100 parts into work. The ratio of these tempera- 

 tures on the work scale is therefore 373 : 273 very nearly. If we decide 

 to make the length of degree on the scale such that there are 100 of them 

 between melting ice and boiling water, then melting ice is at 273 A. 

 (where A denotes the work, or, as it is often termed, the absolute scale), 

 and boiling water is at 373 A. The absolute zero then is at 273 C. or 

 273 absolute degrees below the temperature of melting ice. Though the 

 Carnot engine is ideal merely, and though we can only approximate to 

 it in practice, we shall see in chapter xvii. that we can tell how it would 

 work if realisable. The new scale is, therefore, a perfectly definite one, 

 and it is possible to determine the relation between the work expression 

 of a temperature and its expression on other scales. 



Air and Hydrogen Scales. By the experiments which we shall 

 describe in chapter iv. it has been found that different gases of sufficient 

 tenuity, and sufficiently above their condensing points, expand nearly 

 equally for equal rises of temperature when kept at the same pressure, 

 and that if their density is kept constant their pressure increases nearly 

 equally. Two gases have been chiefly used for thermometric purposes, 

 dry air, and hydrogen, and it is usual to employ the increase of pressure 

 at constant density to give a scale of temperature. Taking Yg^th of the 

 increase between C. and 100 C. to indicate a degree the scale agrees 

 very nearly with the mercury glass scale within that range. A gas 

 thermometer is applicable through a far wider range than the mercury- 

 glass thermometer. Its scale has the further advantage of being nearly 



