THERMODYNAMIC AL SYSTEM OF GIBBS 63 



earth under the influence of gravity. "V^Hien the body falls 

 unimpeded no work is obtained and the whole of its energy is 

 converted into heat when it collides with the earth. If we 

 arrange a pulley so that, in its descent, the falling body raises 

 another mass we shall obtain work corresponding to the weight 

 of the mass raised. There is a limit to the amount of work 

 which can be obtained in this way, for the first body will only 

 continue to fall as long as its weight is greater than that of the 

 body which is raised. The maximum work is obtained when 

 the weight raised is only infinitesimally less than that of the 

 faUing body. In other words, we obtain the maximum work 

 when the force tending to cause the change (in this case, the 

 gravitational force on the falling body) is opposed by a force 

 which is only smaller by an infinitesimal amount. 



Similar considerations apply to changes of other kinds. For 

 example, in the expansion of a gas into an evacuated space, 

 there is no opposing force and no work is obtained; but if the 

 expansion of the gas is opposed by a mechanical force acting on 

 a piston, work is obtained which has a maximum value when the 

 force on the piston is only infinitesimally less than that required 

 to balance the pressure of the gas. When the force on the piston 

 exactly balances the gas pressure, no change occurs; but when 

 the former is reduced by an infinitesimal amount the gas will 

 expand and will continue to do so as long as the applied force is 

 slightly less than that required to balance the gas pressure. 

 Under these conditions we obtain the maximum work from the 

 gas expansion. A change carried out in such a way is called a 

 reversible change, since an infinitesimal increase in the forces 

 opposing the change will be sufficient to make them greater 

 than the forces of the system and will cause the change to 

 proceed in the reverse direction. 



If we take the system of bodies through a complete cycle of 

 operations, so that its final state is identical with its original 

 state, the total energy change is zero, so that by (1), 



2Q - ZTF = ; 



i.e., the algebraic sum of all the quantities of heat absorbed by 

 the system is equal to the algebraic sum of the amounts of work 

 done against external forces. 



