272 Prt'. H. L rallrmlar. On tin- Tln'rm<><! i/num u;il 



The constant value of the ratio r/V along an isentropic Is ^ivcii by 

 the relation, 



which may l>e written in the form, 



c /\ = (cY 



where e is the base of natural logarithms, and the symbols p, c, V, 

 6, </>, refer to a standard state such as C., and 760 nun. 



The Change of Entropy < - <f> in expansion from p to p at a con- 

 stant temperature 6" is deduced from the relation, 



d<f> = (d*t>/dp)edp = -(dv/d6)pdp = -(R/p + ne 9 /P)dp ...... (17), 



whence <f>-<t> = Rlog_p/p + (/> -p^c'/B" ............... (18). 



The Heat Absorbed is given by the expression, 



Q - Q = K,elogp /p + (p -p)nc ............... (19). 



The Work Done, W = R 6" log plp, is the same as for an ideal gas 

 between the same limits of pressure. 



The Change of Intrinsic Energy is, therefore, 



E-E = nc(p-p) ........................ (20). 



Heating at Constant Pressure. 



The Heat Absorbed in a rise of temperature from 6" to 6 at constant 

 pressure p is given by the equation 



Q - Q = JSrf0=S'(0-0 9 ) + (+l)/(e-r) ......... (21). 



Change of Energy, 



E-E = s 9 (0-tf) + np'(c'-r) .................. (22). 



The Work Done, 



W = R(0-6)+p(c e -r) ..................... (23). 



Change of Entropy, 



= s log ofr + n p(c o /e' - c/e) ...... (24). 



In passing from any one state represented by the co-ordinates p, 0, 

 to any other state represented by p, 0, both the change of energy and 

 the change of entropy must be independent of the process by which 



