62 BUTLER 



ART. D 



work which can be obtained from it. Since it is not possible 

 to remove the whole of the heat from a body, or to change it into 

 a state in which we may be sure that no further work may be 

 obtained from it, for practical purposes we may define a stand- 

 ard state in which the energy is taken as zero. Then the 

 energy of a body in any given state is taken as the sum of the 

 quantities of heat and work which must be supplied to bring 

 the body from the standard state into the given state. The 

 energy of a body or system of bodies in a given state is a 

 definite quantity and is independent of the way in which it is 

 brought into that state. For if it were possible for a system of 

 bodies to have different amounts of energy in the same state, 

 it would be possible to obtain energy without the system or any 

 other bodies undergoing change, which is contrary to the 

 Principle of Conservation of Energy. 



Consider two states of a system in which its energy is e' and 

 e". The change of the energy of the system, i.e., the energy 

 which must be supplied from outside, when it passes from the 

 first to the second state, is Ae = e" — e'. Since e" and t' depend 

 only on the initial and final states of the system, Ae is independent 

 of the way in which the change of state occurs. In general, 

 the energy of a system may change (1) by receiving or giving 

 heat to other bodies, and (2) by performing work against ex- 

 ternal forces. If, in a change of state, the system absorbs a 

 quantity of heat Q from outside bodies and performs work W 

 against external forces,* its energy change is 



Ae = Q - PF. (1) 



Now, although the energy change of a system in passing from a 

 given initial state to a given final state is constant and inde- 

 pendent of the way in which the change occurs, the same is not 

 true of Q or W. But of the possible ways of conducting the 

 change, there will usually be one for which PF is a maximum 

 and, therefore, Q also a maximum. 



As a simple illustration, consider the fall of a body to the 



* Heat evolved by the system and work done on the system by ex- 

 ternal forces are counted as negative. 



