Answered: Define about Thermodynamic Identities ?

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Question

Define about Thermodynamic Identities ?

Expert Solution

Step 1

$T h e t h e r m o d y n a m i c i d e n t i t y i s a u s e f u l s u m m a r y r e l a t i o n s h i p t h a t s m a k e s u s e o f t h e p o w e r o f c a l c u l u s a n d p a r t i c u l a r l y p a r t i a l d e r i v a t i v e s . I t m a y b e a p p l i e d t o e x a m i n e p r o c e s s e s i n w h i c h o n e o r m o r e s t a t e v a r i a b l e s i s h e l d c o n s \tan t, e . g ., c o n s \tan t v o l u m e, c o n s \tan t p r e s s u r e, e t c . T h e t h e r m o d y n a m i c i d e n t i t y h o l d s t r u e f o r a n y i n f i n i t e s m a l c h a n g e i n a s y s t e m s o l o n g a t t h e p r e s s u r e a n d t e m p e r a t u r e a r e w e l l d e f i n e d . I t i s p r e s u m e d t h a t t h e n u m b e r o f p a r t i c l e s i s c o n s \tan t$

Step 2

$T h e r m o d y n a m i c i d e n t i t y d U = T d S - P d V w h e r e, U - I n t e r n a l e n e r g y S - e n t r o p h y V - v o l u m e T - t e m p e r a t u r e P - p r e s s u r e d d e n o t e s t h e t o t a l d i f f e r e n t i a l o f t h e a s s o c i a t e d q u a n t i t y .$

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