Prove that dq is not a perfect differential while dq/T is a perfect differential .?
Answers
The antiderivative of a perfect differential would give a function , in case of an imperfect differential a function wouldn't be obtained
In thermodynamics use of imperfect differentials are common , they represent a path dependent infinteseminally small quantity of a patch function which must be integrated along a path rather than between states of the system
One such example is dq ,which is an imperfect differential of a path function heat exchange ( q ) ( i have given a simple proof of q being a path function in the attachment ) , if we simply take the antiderivative of dq , we will not get a function , instead we will have to integrate it along a path which will instead give us the path dependent quantity : heat exchange ( q )
In thermodynamics antiderivative of dq/T represents a function Entropy , here q strictly represents heat exchange in a reversible process , Entropy is a state function , it's differential need not to be integrated along a path , its value depends on the state itself ( i have derived a simple formula taking the antiderivative of dq/T between two states for a simple reversible Isobaric process for reference in the attachment) , So dq/T is a perfect differential which is the differential of a state function entropy .
