Energy and Entropy of a Body. 15 



the external work (Werk) expressed in thermal units 



dw = Apdv S . (28) 



Let us now suppose that the condition of the body is deter- 

 mined by the magnitudes x and y, then v must be regarded as a 

 function of x and y, and the last equation may be written thus, 



dw 7 dw 7 A (dv 7 dv 7 \ 



whence we immediately get the two following equations : 



dw __ . dv 

 dx~~ P dx 

 dw _ . dv 

 dy ~~ P dy 



By introducing these values into the expressions given for E^ 

 and E'^ in (4) and (7), we have 



E ^ =A [|tS)-it|)]' 



y Ldy\T dx) dx\T dy/J 



In the last of these equations we will put, for shortness, 



*r=f, (29) 



whereby it becomes 



^=^[|(-£)-£(4;)]- 



Performing now the differentiation of the products in these ex- 



.' d v d v 



pressions, bearing in mind that -—- = -j-t> we obtain 



** \dy dx dx dy) * ' 



^=Mf •S-S-l)- ■ ■ ■ w 



If it be assumed that one of the independent variables by 

 which the condition of the body is determined (for instance, the 

 variable which we have hitherto denoted by y) is the tempera- 

 ture of the body, all that is needful to do is to write everywhere 



