264 HEAT. 



doing work on the substance represented by ABOD, a certain quantity 

 of heat has been taken from the refrigerator and a quantity exceeding 

 this by the heat equivalent of ABOD has been given to the source. 



Conditions for Reversible Working 1 . In order that the same 



figure may represent the direct and reverse working, that is, in order 

 that indefinitely small changes in the external conditions shall reverse 

 the order of change, certain conditions are necessary. These conditions 

 are 



1. That the working substance shall never differ sensibly in tempera- 

 ture from the bodies to which it is giving or from which it is receiving 

 heat ; for suppose that while the working substance goes along BC in the 

 diagram, the source is at a higher temperature T, then it is impossible to 

 make the working substance return along CB merely by a gradual in- 

 crease of load. The source being T - 1 hotter, the substance cannot 

 yield heat up to it. 



This condition requires that the isothermal parts of the cycle BO and 

 DA should be traversed exceedingly slowly. 



2. That the pressure exerted by the working substance on the piston 

 shall be sensibly equal to the load, for then, and then only, will in- 

 finitesimal changes of load suffice to reverse the direction of motion. 

 This condition requires that the motion shall always be exceedingly 

 slow. 



Some processes, in which kinetic energy is generated by a difference 

 between internal pressure and external load, may be reversible at the 

 initial and final points though not at intermediate points. For example, 

 if a gas is contained in a vertical non-conducting cylinder under a 

 frictionless piston, and if the load is suddenly decreased by a finite 

 amount, the piston will spring up and move out to a certain point, the 

 same, if we can neglect the effect of viscous friction, as if the load had 

 been decreased gradually to that corresponding to the final volume, and 

 the whole change had been adiabatic. At this final point the piston will 

 itself reverse the motion, and will in fact continue to move harmonically. 

 The work done between the extreme points is equal to load x distance 

 moved out. But at intermediate points, the motion evidently is not 

 reversible by an infinitesimal change of load. 



3. That the machinery moves without friction. If there is friction 

 the load will have to be altered by a finite amount to reverse the motion. 

 The heat generated by the friction is also " irreversible," for it will be 

 given up by the working substance to the surroundings, whether the 

 motion is direct or reverse. 



Examples Of Reversible Processes. It will be realised from the 

 foregoing that exactly reversible processes are ideal, in that exact reversi- 

 bility requires exact equilibrium with surroundings, that is, requires .a 

 stationary condition, while a process is necessarily a changing condition. 

 But we can approximate as closely as we like to the conditions of 

 reversibility, by making the conditions as nearly as we like those re- 

 quired, and lengthening out the time of change. 



As an illustration, imagine a quantity of water at 100 0. under a 

 piston loaded to 1 atmosphere. Imagine the cylinder to be kept exactly 

 at 100 0. by, say, a current of steam round its outside. There will be 

 equilibrium. But if we decrease the load ever so little, a minute bubble 



