A relation between entropy and free energy change for metals
- PDF / 176,943 Bytes
- 2 Pages / 612 x 792 pts (letter) Page_size
- 75 Downloads / 203 Views
THERMODYNAMICALLY
a s y s t e m is in e q u i l i b r i u m when the f r e e e n e r g y is m i n i m u m . The e n e r g y and e n t r o p y functions can be c o n s i d e r e d as m a t h e m a t i c a l f o r m u l a t i o n s of two opposing t e n d e n c i e s in the s y s t e m . On the one hand a s t r i v i n g for a m i n i m u m e n e r g y and on the other hand a s t r i v i n g for a m a x i m u m entropy. Although the v a r i o u s equations r e l a t i n g t h e s e p a r a m e t e r s a r e well-known, a f u r t h e r study of t h e i r r e l a t i o n s r e v e a l s some i n t e r e s t i n g t h e r m o d y n a m i c p h e n o m e n a which a r e p r e s e n t e d in this p a p e r . BASIC ANALYSIS The free e n e r g y u n d e r i s o t h e r m a l and i s o b a r i c conditions as is u s u a l in alloy e q u i l i b r i a , is defined as GT = HT- TST [1] where G T , H T and S T a r e the Gibbs f r e e e n e r g y , enthalpy and e n t r o p y r e s p e c t i v e l y at a t e m p e r a t u r e T. F r o m the T h i r d Law of t h e r m o d y n a m i c s where entropy is z e r o at 0 K for a p e r f e c t c r y s t a l l i n e subs t a n c e , one can d e r i v e the following t h e r m o d y n a m i c function @ at T
ST
--
[(H T - H o ) / T ]
[2]
where Go and H0 r e f e r to the v a l u e s at 0 K. The i m p o r t a n c e of ~b-function is obvious in t h e r m o d y n a m i c s and will be d i s c u s s e d l a t e r on. The o r i g i n of the above r e l a t i o n s can be p r e s u m e d to be the c o n s e q u e n c e of the s i m i l a r t e m p e r a t u r e dependence of G T - Go and S T - So on the b a s i c p a r a m e t e r s such as Debye t e m p e r a t u r e , e l e c t r o n i c specific heat, d i l a t a t i o n t e r m s and so forth, together with the a p p r o x i m a t e l y c o m p e n s a t o r y effects of f Cp dT and T in G T - Go functions where Gp is the heat capacity. Due to the dependence of q3T and S T on the C p - f u n c t i o n s , an i n t e r r e l a tion between them can be i l l u s t r a t e d in the following way. The equation for the total e n t r o p y of a m e t a l u n d e r g o i n g no phase t r a n s f o r m a t i o n s is given by
f (CpYT)dT
S T = So +
(Cp/T) dT. 0
On the b a s i s of the T h i r d Law of t h e r m o d y n a m i c s where So = 0, one gets BIVABASUCHATTERJEE is Senior Scientist, The British Aluminium Co. Ltd., Chalfont Technological Centre, Chalfont Park, Gerrards Cross, Buckinghamshire,U. K. Manuscript submitted February 11, 1977. METALLURGICALTRANSACTIONSA
0
F r o m Eq. [2] the qS-function can be r e l a t e d to the Cpfunction as $T = [ fT(cp/T)
HT] - ( l / T ) f T c p
0
where
dT
[4]
o
f Tcp d T
= H T - Ho. A r e l a t i o n between S T and
0
~)T is evident f r o m Eqs. [3] and [4] b e c a u s e the a c t u a l Cp - T r e l a t i o n s h i p for m e t a l s can be r e p r e s e n t e d by a s i m p l e e x p r e s s i o n involving the s a m e powers of T. The a i m of the p r e s e n t paper is to e s t a b l i s h
Data Loading...
