Class 11 Chemistry Gases & Solutions States of Matter

Show that the differential $dV$ of the molar volume of an ideal gas is an exact differential and hence $V$ is a state function.

Solution:

$V=PRT $

For $dV$ to be exact differntial,

$δTδ (δPδV )=δPδ (δTδV )$

$δTδ (δPδV )=δTδ (p_{2}−RT )=P_{2}−R $

$δTδ (δTδV )=δPδ (PR )=P_{2}−R $

$δTδ (δPδV )=δPδ (δTδV )=P_{2}−R $

So, $dV$ is an exact differential.

Volume is a state function because the volume is only dependent on the final and initial values and not on the path taken to establish those values.

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