Comment whether the following quantities can be called as properties o

1.	Comment whether the following quantities can be called as properties or not :(i) \(\int pdV\)(ii) \(\int Vdp,\)and(iii) \(\int pdV\) + \(\int Vdp\).
Answer» (i) \(\int pdV\): p is a function of V and integral can only be evaluated if relation between p and V is known. It is thus an inexact differential and hence not a property. (ii) \(\int Vdp,\): It is not a property for the same reason as mentioned in (i). (iii) \(\int pdV\) + \(\int Vdp\). \(\int pdV\) + \(\int Vdp\) = \(\int pdV\) + Vdp = \(\int\) d(pV) = pV. Thus the integral can be evaluated without knowing the relation between p and V. It is an exact differential and hence it is a property.

Comment whether the following quantities can be called as properties or not :(i) \(\int pdV\)(ii) \(\int Vdp,\)and(iii) \(\int pdV\) + \(\int Vdp\).

Answer»

(i) \(\int pdV\):

p is a function of V and integral can only be evaluated if relation between p and V is known. It is thus an inexact differential and hence not a property.

(ii) \(\int Vdp,\):

It is not a property for the same reason as mentioned in (i).

(iii) \(\int pdV\) + \(\int Vdp\).

\(\int pdV\) + \(\int Vdp\) = \(\int pdV\) + Vdp = \(\int\) d(pV) = pV.

Thus the integral can be evaluated without knowing the relation between p and V. It is an exact differential and hence it is a property.

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