520 F. II. Bigelow — Thermodynamics of the 



(Qi — Q ) term is a large one, especially in the higher strata, as 

 will be seen from the accompanying examples, and this cannot 

 ever be computed with a constant specific heat Cp and gas 

 coefficient 11. At present there seems to be no method of 

 computing (Q, — Q„) independently of i(q\— qf), hut as the circu- 

 lation can be determined by observations of the velocity in the 

 different strata, we have, 



(32) (Q-Q.) - (Cp.-CpJ (T a -T ) - * (ql-qt). 



It also follows that observations which contain the height s, 

 the pressure P, and the temperature T, but omit the velocity 

 of circulation and the direction of motion q, are useless in 

 problems of dynamic meteorology. If, furthermore, the 

 relative humidity is omitted, there is no way of studying the 

 constituents of the radiation (Q l — Q ), and the parts depending 

 upon dry air and aqueous vapor respectively. 



Entropy, Work, Inner Energy, Radiation Function, 

 and Exponent of Radiation. 

 Having derived the values of (Q x — Q„) through computations 

 based upon observations, we can proceed to compute the funda- 

 mental thermodynamic terms applicable to a nonadiabatic 

 atmosphere by the following formulas, where v is volume of 

 unit mass, Cv and Qp are the specific heats of air at constant 

 volume and constant pressure. 



Entropy. 



(33) S 1 -S i = ^^ = n 1 Cp.^-log-^-^-B li log^. 



(T —T) 1 P 



io - r o 



External Worh. 



(34) W-W, = P 10 (v-v ) = R„ (T.-T.) - -^ 



= 0,.^(T.- T ,-^=(V- 1 )^. 



Internal Energy. 



(35) 11,-17= C Wl „(T a -T ) =(C A -R 10 ) (T.-TJ = 



(C/>. - Cp I0 ^=±) (T.-T.) = Cp> (T„-T ) 



Heat Energy. 



(36) Q-Q B =Ci> 10 (T a -T.) +P 10 (v-v B ) = T 10 (S-S ) 



= (Cp^-CpJ (T.-T ) = Op. (T.-T.) - *^ 



k-l P-P 



