68 BUTLER 



ART. D 



The integral, / dQ/t has therefore the same value for all re- 



versible paths by which the system may be changed from state 

 (7) to state (//). Its value for a reversible path is thus a definite 

 quantity, depending only on the initial and final states of the 

 system, and it may be regarded as the difference between the 

 values of a function of the state of the system in the two states 

 considered. This function was termed the entropy of the 

 system by Clausius in 1855. We may therefore write: 



•(") dQ 



= V' — 1 



t 



(2) 



where 77^ and rj'^ are the values of the entropy in states (/) and 



For an infinitesimal change of state, (1) may be written in 

 the form: 



de = dQ - dW. 



Now if the change of state is reversible, according to (2), dQ = 

 tdrj ; also if the work is done by an increase of volume dv against a 

 pressure p, dW = pdv, so that 



de = tdr] — pdv. (3) 



We may observe that all infinitesimal changes of state of a 

 system, which is in equilibrium, fulfil the condition of reversi- 

 bility, for equilibrium is a state in which the forces of the 

 system are balanced by the opposing forces, and in an infinites- 

 imal change the system can only be removed to an infinites- 

 imal extent from a state of equilibrium. Equation (3) there- 

 fore applies generally to infinitesimal changes of a system 

 which is in a state of equilibrium. 



We will now consider the changes of a system of bodies in 

 relation to the changes which necessarily occur in surrounding 

 bodies. When the sytem undergoes a reversible change from a 

 state (7) to a state (77), the entropy change, as we have seen, is: 



r^u -n^ ^ \ dQ/t, 



