POTENTIAL TEMPERATURE AND ENTROPY BAUER 



497 



have for certain cases an easy graphical representation of the 

 entropy function. 



In the pv diagram, fig. i, let aa' and bb' represent portions of 

 two adiabats, and o'a'b' be the line of standard pressure p = p . 



FIG. I. 



Suppose the initial thermodynamic state of the body experi- 

 mented upon be represented by the point a and some process ab be 

 carried out. According to definition, the potential temperature, 

 6 a , in the state a will be the temperature at the point along the 

 adiabat aa' where it is intersected by the line of standard pressure. 

 But according to equation (2) the temperature at this point, a', 

 is proportional to the volume, i.e., to o'a' . Similarly the potential 

 temperature in the state b will be proportional to the abscissa o'b' . 

 Hence if measured on the same scale, o'a' and o'b' will represent 

 directly for the same substance the respective potential tempera- 

 tures. It is thus easy to represent graphically at any stage of the 

 process ab the corresponding potential temperature. 



If it is desired to determine the numerical value of the potential 

 temperature, this can be done with the aid of the equation of the 

 adiabat thus: 



-,' — j /1 



= T„ 



Pa 



£-1 



£ 



or 



PoV a 



\ £- 1 1 



£- 1 1 



e T„ = k'v„ e T 



(3) 



where e = 1.41 



For a perfect gas, the entropy, s, per unit of mass may be ex- 

 pressed by the following equation: 4 



4 See, e. g., Planck's Thermodynamics. 



