Monday, 22 August 2016

thermodynamics - Why $dW=pdV$ is an inexact differential?


I remember an exact differential as:


$$A=M(x,y)dx+N(x,y)dy $$


and the condition for be exact is:


$$\frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}. $$



Can I use that definition to proof that $dW=pdv$ is not an exact differential?


I was thinking in use $W=W(p,V)$ and calculate


$$dW=\frac{\partial W}{\partial p}dp+\frac{\partial W}{\partial V}dV$$


and try to find a way to refute the idea of an exact differential for $pdV$. Am I right?




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