THERMODYNAMICS. 



275 



Now if BDA is described in the reverse direction ADB, heat taken in 

 becomes heat given out and we must change the sign of Q in the second 

 term of Ahe left side of the equation. Changing the sign and transposing 



2^ from A through to B 2~ from A through D to B 



V 



or the entropy received by either path is the same. 



The Adiabatics are Isentropics. If a body is compressed or expanded 

 adiabatically, i.e. so that, whatever energy may be transferred as work, 

 none is conducted as heat, the entropy remains constant and the adia- 

 batics on the indicator diagram are lines of equal entropy, or isentropics. 

 The different adiabatics may be 

 denoted by the value of the entropy 

 along them, reckoned from some 

 standard condition, just as the dif- 

 ferent isothermals are denoted by 

 the value of the temperature along 

 them. The entropy of a body is 

 usually denoted by <f>. 



The Entropy Temperature 



Diagram is a diagram in which 

 the ordinate represents the tempera- 

 ture, and the abscissa the entropy 

 reckoned from some standard con- 

 dition. 



If AB (Fig. 158) represents a 

 small change of condition of a body, 

 on an entropy temperature diagram, FIG. 158. Entropy-Temperature 

 the temperature changing from AM Diagram, 



to BN and the gain of entropy being 



MN, and if Q be the quantity of heat received in the change from A 

 to B 



Q 



H 



entropy 



M N 



Q = MN. 



= area ABNM. 



Similarly for every element in a finite change. Then the heat received 

 in a change from P to Q is equal to the area PQKH. 



Now if we take a body through any cycle, returning to the original 

 state the entropy and temperature both have their original values, and 

 a cycle is therefore represented by a closed curve on the diagram. The 

 area included by the curve is the difference between the heat taken in 

 and the heat given out, and so represents the amount of heat transformed. 

 We shall make use of the diagram later, but without further discussion 

 now, the reader will see that a Carnot's cycle is represented by a rect- 

 angle with sides parallel to the axes, and he may easily prove that for a 



