EQUATIONS OF FOG CHAMBER. 



53 



46. Exhaustion difficulties. As the stopcock was not tight internally, 

 the final or isothermal pressure in the fog chamber could not be regis- 

 tered. In any case it is doubtful whether the cock can be elosed again 

 quickly enough. It was therefore customary in the following experi- 

 ments to put the vacuum chamber and the fog chamber in contact for 

 a short time, after isothermal conditions had been reestablished. Long 

 communication between the fog chamber and the vacuum chamber is 

 unadvisable from other points of view, since the character of the nuclea- 

 tion of the latter is not so well guaranteed It is therefore necessary 

 to ascertain the conditions under which exhaustion takes place. 



Let v be the volume of the fog chamber, V the volume of the vacuum 

 chamber, k/c the ratio of specific heats of the moist gas, and let p, v, x, p, 

 denote its pressure, volume, absolute temperature, and density, under 

 conditions given by the subscripts. It will be convenient to refer 

 to the vacuum chamber by the same symbols with accents. Hence the 

 successive thermal states will be for drv air, 



For the fog chamber. 



For the vacuum chamber , 



Initially = 7^'> 



Adiabatically (alone) />, 



Isothermally(alone) p, 



Isothermally (together) ... p B 



Initially />' 



Adiabatically (alone) .... p\ = p l 



Isothermally (alone) .... p' 2 



'[ Isothermally (together) . . p' 3 = p 3 



T 



T l 

 T= T 



T 3= T 

 T'=T 



t' 2 = t 



p 

 Pi 



Pi"* Pi 

 Pa 



P' 



P\ 



P^P'i 



P\ = P 3 



The equations describing the transformations are (again for dry air) : 



(k-c)/k T /-b'\{k-c)/k 



i- (0 



A U) 



p =Rpr p' -JRp't 



p, = Rp x T v P'i=Rp\t 



p 2 = Rp 2 r = R Pl T p' 2 =Rp' 2 T = Rp' lT 



p 3 = Rp 3 T Or p 2 jp' 2 = P2/P' ' 1 



3 pv + p l V = p{V + p' \V = p 2 v + p'\V = p 3 (v+ V) 



From these one may deduce, relative to the value of p v 

 v (p(Jk-c]/kpc/k^ p 3 ) = y (p 3 _ p'(k-c)/k pc/k) 

 or 



PAi+v/V) 



4 Pl = p'(k-c)/k + ( v / V ) p (k-c)/k 



5 P'i+p2 -v/V = p 3 (i +v/V) 



