APPENDIX 367 



enter it during this act of expansion. The expansion 

 is therefore adiabatic ; the temperature falls from 

 T 2 to 7\ ; and work is done by the gas. 



Second operation, (2->3). The piston is now at the 

 position I, that is, at the upper end of its stroke, and 

 we must bring it back again to the lower end of the 

 cylinder. The valve is turned so that the bottom of 

 the cylinder is placed in thermal communication with 

 the refrigerator ( - ) , and the piston is pushed in to the 

 position II. The gas is therefore compressed until its 

 volume decreases from a point beneath 2 to a point 

 beneath 3. As it is being compressed, heat is generated 

 and its temperature would rise, but as this heat is 

 generated it flows into the refrigerator, so that the 

 temperature of the gas remains the same during the 

 operation. The contraction is therefore an isothermal 

 one ; the temperature remains at 7^ ; and work is 

 done on the gas from outside. 



Third operation, (3^-4). But the piston is not 

 at the lower end of its stroke yet. We turn the valve 

 so that the bottom of the cylinder is closed by the 

 non-conducting plug 0, and then push in the piston 

 until it reaches the position III. The gas is still 

 further compressed, and this compression generates 

 heat. But the heat cannot escape, so that the tempera- 

 ture of the gas rises until it reaches r 2 . The con- 

 traction is therefore an adiabatic one. Work is done 

 on the gas. 



Fourth operation, (4-^1). The piston is now at the 

 lower end of its stroke. We turn the valve so that the 

 bottom of the cylinder is placed in communication 

 with the source of heat (+). The gas expands from 

 the point beneath 4 to the point beneath i, raising 

 the piston to the position II. This expansion of the 

 gas would lower its temperature, but it is in com- 



