FREE BOOKS

Author's List




PREV.   NEXT  
|<   101   102   103   104   105   106   107   108   109   110   111   112   113   114   115   116   117   118   119   120   121   122   123   124   125  
126   127   128   129   130   131   132   133   134   135   136   137   138   139   140   141   142   143   144   145   146   147   148   >>  
econd by unit area of the cathode. Thus the number of positive ions produced in the layer is [alpha]i0[epsilon]^[alpha]x dx. If these went straight to the cathode without a collision, each of them would have received an amount of kinetic energy Vex/d when they struck the cathode, and the energy of the group of ions would be Vex/d.[alpha]i0[epsilon]^dx dx. The positive ions will, however, collide with the molecules of the gas through which they are passing, and this will diminish the energy they possess when they reach the cathode. The diminution in the energy will increase in geometrical proportion with the length of path travelled by the ion and will thus be proportional to [epsilon]^-[beta]x, [beta] will be proportional to the number of collisions and will thus be proportional to the pressure of the gas. Thus the kinetic energy possessed by the ions when they reach the cathode will be [epsilon]^{-[beta]x} . V(ex/d) . [alpha]i0[epsilon]^{[alpha]x} dx, and E, the total amount of energy in the positive ions which reach the cathode in unit time, will be given by the equation _ /d E = | [epsilon]^{-[beta]x} . V(ex/d) . [alpha]i0[epsilon]^{[alpha]x} dx _/0 _ Ve[alpha]i0 /d = ----------- | [epsilon]^{-([beta]-[alpha])x}.x.dx d _/0 Ve[alpha]i0 / 1 / 1 d \ \ = ----------- { ------------------ - [epsilon]^{-([beta]-[alpha])d} { ------------------ + ---------------- } } (1). d \([beta]-[alpha])^2 \([beta]-[alpha])^2 ([beta]-[alpha])/ / If the number of corpuscles emitted by the cathode in unit time is proportional to this energy we have i0 = kE, where k is a constant; hence by equation (1) we have ([beta]-[alpha])^2 d V = ------------------ . --, ke[alpha] I where I = 1 - [epsilon]^{-([beta]-[alpha])d} (1 + d([beta] - [alpha])). Since both [beta] and [alpha] are proportional to the pressure, I and ([beta] - [alpha])^2d/[alpha] are both functions of pd, the product of the pressure and the spark length, hence we see that V is expressed by an equation of the form 1 V = -- [int](pd) (2), ke where [int](pd) denotes a f
PREV.   NEXT  
|<   101   102   103   104   105   106   107   108   109   110   111   112   113   114   115   116   117   118   119   120   121   122   123   124   125  
126   127   128   129   130   131   132   133   134   135   136   137   138   139   140   141   142   143   144   145   146   147   148   >>  



Top keywords:
epsilon
 

energy

 

cathode

 
proportional
 
positive
 
number
 

pressure


equation

 

length

 

kinetic

 
amount
 
denotes
 

constant

 

corpuscles


emitted

 

expressed

 

functions

 

product

 

produced

 

straight

 
diminution

increase

 

geometrical

 
proportion
 

possess

 
diminish
 
passing
 

collide


travelled

 

molecules

 

collision

 

received

 
possessed
 
struck
 

collisions