THERMODYNAMICS. 



259 



through any process by which it returned finally to the same volume, 

 but was appreciably colder, and if it had meanwhile produced a balance 

 of work, then the second law would be untrue.* 



The application of this principle will enable us to find the maximum 

 fraction of heat which under given conditions can be transformed to 

 work, and will further give us the temperature changes occurring when 

 bodies undergo known strains or are subjected to known stresses. 

 Incidentally, it will give us a scale of temperature which is definite 

 and quite independent of any particular substance Lord Kelvin's 

 work scale. 



As our investigations will be carried out chiefly by the aid of the 

 Indicator Diagram, we shall first give some account of that diagram as a 

 mode of setting forth the conditions of a body and the relations between 

 its temperature, pressure, and volume. 



The Indicator Diagram. In this diagram two axes at right angles 

 are chosen as volume and pressure axes respectively. A point on the 

 diagram represents by its ordinate the pressure of the body, supposed to 

 be uniform throughout, and by its abscissa 

 the volume. Thus in Fig. 147 A represents 

 the condition of a body which has volume OM 

 and pressure AM. 



If any change occurs in the body the 

 successive conditions may be represented as 

 regards pressure and volume by a series of 

 points which will together form a line either 

 straight or curved, joining the points repre- 

 senting the initial and final conditions, as 

 APQB in Fig. 147. 



We may represent the work done by or on 

 a body during a change of volume by an area 

 on the diagram. Let S (Fig. 148) represent 

 the surface of the body when in the condition represented by P on the 

 diagram, and let S' represent the surface when the body is in the con- 

 dition Q very near P, so that S' is only very slightly larger than S. Let 

 a be a small area on S, which has moved against the pressure through a 

 distance d. 



If p and p' are the initial and final pressures, the change is so small 

 that we may suppose the pressure to vary uniformly from p to p'. Then 

 the mean pressure is ^(p +p), and the work done is ^(p +p')a.d. Summing 

 up all over the surface, the total work 



FIG. 148. Work done by 

 a Body in Expansion. 



P+P' 



"2, ad. 



= x volume between S and S'. 

 2 



p+p' . . , 



mt-*~- x increase in volume. 



* A statement less general but sufficient for our purpose in Thermodynamics 

 would be : We cannot by a cyclical engine derive work continuously by conducting 

 heat into the engine from the coldest part of the surroundings. 



