260 



HEAT. 



But 



p +p PH + QK . 



in Fig. 147, 



and increase in volume 

 Therefore, total work 



2 



= HK 

 PH + QK 



xHK 



= area of slip PK. 



The total work from A to B is evidently the sum of all such slips, or the 



area AMNB. 



This work represents the energy given out by the body merely 



through expansion against the outside pressure. If the body contracts, 



moving, say, from B to A, the same area will represent the work done 



011 the body, or the energy given into 

 it through contraction under outside 

 pressure. If the point representing 

 the condition of the body moves from 

 A to B and back again along the 

 same course, evidently, on the whole, 

 no external work is done, the two 

 quantities being equal and opposite. 

 But if the return course is not 

 the same, we may have a balance 

 left over. 



Suppose that the body goes 

 along ACB (Fig. 149), returning 

 along BDA. Marking work done 

 by by shading thus ///, and 



volume 

 FIG. 149. Work done in a Cycle. 



work done on by shading thus 

 \\\, where there is a cross 

 shading the two neutralise each 

 other, and the balance of work done 

 by the body is represented by the 



area included by the curve ACBDA. Had the change of condition been 

 represented by a counter-clockwise motion round the curve, the same 

 area would have represented the work done on the body. A clockwise 

 motion round the area then represents the giving out of so much energy. 

 Isothermals. If the temperature of a body is kept constant, for 

 each pressure there is in general a single definite value for the volume, 

 and the relation between volume and pressure will be represented by 

 a curve. For instance, in the case of a gas p x v is nearly constant for 

 a given temperature, and the curve will be nearly an equilateral hyper- 

 bola. Such a curve is termed an isothermal. We may draw a series of 

 isothermals, each corresponding to a different temperature. The reader 

 can easily plot the isothermals for a gas at 0., 100 C., and 200 on 

 the assumption that pv = RT when T is the temperature on the gas scale 

 and K is a constant for a given gas. 



The isothermals for liquids and solids are in general nearly parallel 

 to the pressure axis. Thus for water an isothermal as it rises will only 

 approach the pressure axis by --- of the volume for an increase of 1 



