Chapter 3 73
about 200 seconds» T h e re fo re th e f i n a l mean gas te m p e ra tu re s a r e ab o u t 25^0 and 235^0 f o r f o rc e d and f r e e c o n v e c tio n c o o lin g r e s p e c t i v e l y . F i n a l l y , th e h e a t l o s s by r a d i a t i o n a t 235°C from th e tube o u t e r w a ll i s , by S te fa n * s Law, about 0.3W and i s t h e r e f o r e n o t an im p o rta n t l o s s p r o c e s s i n t h i s c a s e .
3 .2 .2 D i f f u s i o n
Having d e term in ed th e te m p e ra tu re c o n d itio n s p r e v a i l i n g i n th e system we can now c o n s id e r th e d i f f u s i o n o f f l u o r i n e , th ro u g h th e h e liu m ~ flu o rin e donor m ix tu re , t o th e tube w a l l s . I t w i l l be assumed t h a t each microwave p u ls e c o n t r i b u t e s a c o n s ta n t c o n c e n t r a t io n 0^ o f f l u o r i n e by d i s s o c i a t i o n o f a donor m o le c u le . The tim e b e h a v io u r o f th e s p a t i a l d i s t r i b u t i o n f o llo w in g a s i n g l e microwave p u lse i s g iv e n d i r e c t l y by e q u a tio n s (9) and (19) as shown i n B’i g 3 . 3 where th e te m p e ra tu re s c a l e (1 ~ 2) i s r e p la c e d by th e c o n c e n t r a t io n s c a l e 0 - Cq, S i m i l a r l y , F ig 3 .4 g iv e s th e s p a t i a l mean c o n c e n t r a t i o n a g a i n s t d im e n s io n le s s tim e on a s c a l e 0 - f o llo w in g à s i n g l e p u l s e . The mean c o n c e n t r a t i o n a f t e r many p u ls e s i s found by r e - w r i t i n g (31) i n t h e form
= 6 7 .1 (1 “ , (38)
The e q u ilib r iu m v a lu e from (32) i s
E q u a tio n (29) f o r th e d i f f u s i o n c o e f f i c i e n t i s e v a lu a te d w ith as th e helium atom ic mass and th e mean f l u o r in e - h e l i u m d ia m e te r , u s in g v a lu e s from T able 3 , 1 , t o g iv e
D = 2.01x10"^T ^^^/P mfs°1 , (40)
Using 6 t = 2,5x10**^, we g e t
5 t = a^Ôt/D = 0 .1 2 P /T 3 /2 s ^ (41)
and t h e number o f c a l c u l a t i o n in cre m e n ts per microwave i n t e r - p u l s e p e rio d becomes
n = 7 .3X10” ^T^'^^/P . (42)
V alues o f n when T = 293K a r e g iv e n i n Table 3 . 2 , Combining (39) and (42) g iv e s th e e q u ilib r iu m c o n c e n t r a t io n as
c^ = g uP xio^p/T ^/z , (43)
The e q u ilib r iu m te m p e ra tu re r i s e when th e w a ll te m p e ra tu re i s 293% i s 21°C. Using T = 314K i n (43) a t th e fo u r p r e s s u r e s o f i n t e r e s t g iv e s th e e q u ilib r iu m c o n c e n t r a t io n s f o r th e 293K w a l l te m p e ra tu re . These a p p e ar i n T able 3 . 2 . To o b t a i n th e t e m p o r a l - s p a t i a l mean c o n c e n t r a t io n i n c r e a s e w ith p u ls e number, a mean te m p e ra tu re o f 314K i s used i n (42) ( t h e c o rre sp o n d in g v a lu e s o f n a r e g iv e n i n Table 3 .2 ) and e q u a tio n (3 8) i s th e n u se d . These r e s u l t s a r e p l o t t e d i n F ig 3*9» With f o rc e d c o n v e c tio n , th e e q u ilib r iu m mean gas
j - r r i