96 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



any reference to the heat reservoirs. It contains the following 

 proposition : 



"If a homogeneous body by suitable treatment is allowed to 

 pass through a series of continuous states of equilibrium and 

 thus finally to come back to its initial condition, the summation 

 of the differential, 



dU+pdV 



T ' 



for all the changes of state will be equal to zero. From this follows 

 at once that if the change of state is not allowed to continue to 

 the restoration of the initial condition (i), but is stopped at any 

 state (2), the value of the sum 



rdU+pdV 

 T > ...... 



will depend solely on the final state (2) and on the initial state 

 (i), and not on the course of the passage from i to 2." 1 



11 The last expression is called by CLAUSIUS the entropy of 

 the body in state 2, referred to state i as the zero state. The 

 entropy of a body in a particular state is, therefore, like energy, 

 completely determined down to an additive constant depending 

 on the choice of the zero state." 



(14) " Let us again designate the entropy by S, then 



-f 



dU+pdV 

 T 



1 This is evident from the fact that the quantities U, p, V, and T, under the 

 integral are each a function of the state only and do not depend on its past history. 

 This falls far short of being true for turbulent states, for which it is difficult to 

 get p and T. PLANCK does not make the preceding statement, but gives instead 

 a rigorous proof based on cyclical considerations. 



