THERMODYNAMICS. 



263 



gradually decrease the load, allowing slow expansion. In general a 

 substance tends to cool on expansion, but the substance is here in contact 

 with a conductor maintained at tf, from which it will take in heat, and if 

 the change is slow enough, the temperature of the working substance 

 will never fall sensibly below t. When some arbitrary point C is reached 

 we slide the cylinder back on to the non-conducting table, and then 

 gradually unload the piston, the substance expanding adiabatically till 

 the temperature has fallen again to t', the state being now represented by 

 D. Finally we slide the cylinder on to the refrigerator and increase the 

 load. In general, compression tends to raise the temperature of a 

 substance, but we must here effect it so gradually that all excess of heat 

 is conducted away to the refrigerator and the temperature never rises 

 sensibly above t'. When the pressure arrives at its original value the 



FlG. 151. Carnot's Cycle. 



volume is alro at its original value since the temperature is the same, or 

 the state of the body is again represented by A. 



The balance of external work done by the working substance is 

 represented by the area ABOD, and this is the mechanical equivalent of 

 the excess of the heat taken from the source over that given to the re- 

 frigerator, for the substance in the cylinder has exactly the initial 

 amount of energy and the only changes are in the source and refrigerator. 



The process is reversible, i.e. we might work counter-clockwise round 

 the cycle ABCI), first sliding the cylinder on to the refrigerator and 

 taking in heat from it during a sensibly isothermal expansion, this heat 

 being equal in amount to that given up in the direct working, then 

 sliding it on to the table and compressing adiabatically till the tempera- 

 ture is t, then compressing isothermally till B is reached, giving up to 

 the source heat equal to that taken in in direct working, and finally ex- 

 panding adiabatically till we have the initial temperature, volume, and 

 pressure. In each part of the cycle the work done is equal and opposite 

 to the work done in the same part during the direct working. Then by 



