THERMODYNAMICS. 277 



If the charge is allowed to pass by an insulated conductor to a lower 

 potential, 



Energy transformed = charge x fall in level. 



Then charge corresponds to entropy and potential to temperature. 



Entropy Tends to Increase. These analogies are not to be pursued 

 too far, for while mass and electrical charge (taking into account the whole 

 field) are constants, entropy is only constant in the very special case of 

 reversible transformation, when the maximum amount of heat is converted 

 into other forms of energy. In other cases it tends to increase. When- 

 ever there is any conduction between bodies at a different temperature, 

 there is a gain of entropy, for the hotter one loses Q at 6 V and the cooler 



gains Q at 2 ; the one loses entropy ^, while the other gains entropy 



i 



~, which is greater. If, then, the source is sensibly hotter than the work- 



2 



ing substance, or if the refrigerator is sensibly cooler, there is an increase 

 of entropy. Or if friction occurs, some of the mechanical work goes to 

 produce heat and the body receiving it gains entropy, which is not lost 

 by any other body, but which starts into existence through the friction. 



Now in actual engines there is always conduction going on through 

 finite differences of temperature and there is always friction, so that 

 there is always gain of entropy. 



And more generally in any change of condition of a body, there is no 

 loss and usually a gain in the sum total of entropy. If the body expands 

 or contracts along an adiabatic, then the entropy is unchanged. But if 

 it changes in any other way, heat must be taken in or given out by con- 

 duction. The entropy would only remain unchanged in amount (though 

 passed on from one body to another) if the conduction went on between 

 bodies at sensibly the same temperature. In practice there is always a 

 finite temperature slope, and always therefore a gain in the entropy of 

 the heat conducted. 



On the whole, then, entropy tends to increase. This principle was 

 first laid down by Clausius. 



If we compare transformations from heat with other transformations, 

 we at once notice a marked contrast. In heat transformation there is a 

 constant tendency on the part of the transformed energy to revert to the 

 original heat form, and there is a tendency for it to pass from one body 

 to another by conduction without transformation. But with gravitation 

 energy, for instance, we may allow a mass to fall from one level to 

 another, transforming all the available potential energy to other kinds to 

 the utmost possible extent, though not necessarily to useful forms, and 

 there may be no tendency of the transformed energy to revert to the 

 potential form. Or with electrical energy we may allow a charge to 

 pass from one conductor to another and obtain all the available electrical 

 energy as work or heat. There is nothing in either case corresponding 

 to conduction of heat without transformation. Whenever a rearrange- 

 ment of mass or of electricity occurs without communication /from the 

 outside, there is a loss of potential energy or of electrical energy. 



If we could imagine a frictionless machine in which a mass descending 

 to a lower level lifted up another mass from the absolute zero level to 



