THERMODYNAMICS. 



279 



8 



the absolute zero isothermal a/?y. Of course we have no experimental 

 justification for drawing this isothermal, but for diagrammatic repre- 

 sentation we may suppose it to exist. 



Taking the substance round the cycle AB/3aA, the whole of the heat 

 taken in along AB will be converted into work since no heat will be 

 given out along (3a, its temperature being zero. Then the area AB/3a 

 represents the heat taken in along AB. The external work done along 

 AB is ABNM. Then the gain of intrinsic energy along AB is 



ABaA - ABNM 

 = PB/3aP-APNM 



or if y be a point at some distance along a/3 and yQ the ordinate, adding 

 PayQNP to each, the gain of intrinsic energy is 



B/3yQNB - APa^yQMA. 



The change in the intrinsic energy is represented then by the change in 

 the area AMNQy/3aA. 



Available Energy. The amount of energy in a body or system 

 which can be transformed to useful 

 work depends entirely on the condi- 

 tions under which the work is to be 

 done. 



If we have, for example, a sub- 

 stance in an envelope under pressure, 

 and we can allow it to expand to a 

 given lower pressure, the work done 

 will depend on the nature of the 

 envelope. If it allows heat to pass we 

 shall get more work by an isothermal 

 than by an isentropic or adiabatic 

 expansion. For the adiabatics on the 

 indicator diagram, as we shall see 

 later, are always steeper than the 

 isothermals, so that, if in Fig. 160, AB 

 is the isothermal, AC the adiabatic through A, the work ABNM is 

 greater than the work AOPM. Of course the body in the first case 

 may have taken in energy through the envelope, and may have con- 

 verted some of this to work. 



If the envelope is non-conducting, then the most work will be done if 

 the external pressure differs only by an infinitely small amount from 

 the internal pressure, so that the expansion will be adiabatic. For if 

 there is a finite difference, kinetic energy will be generated in the sub- 

 stance, which will ultimately tend to become heat, and some of the 

 energy will thus be lost for transformation to work. 



Thus, in the gas engine, in which a mixture of coal-gas and air is 

 ignited with transformation of chemical energy to heat, the temperature 

 and pressure of the gas are raised. Obviously the cylinder should be 

 non-conducting, otherwise heat will pass out of the gas which might be 

 transformed. And the expansion should be adiabatic till the pressure 

 is as near as possible to the air pressure, the lowest available. 



The Available Energy of an Isolated System. If we have a system of 



M P 

 FIG. 160. 



