10.7. By invoking the condition for an exact differential, Eq. (10.30), demonstrate that the reversible heat Or is not a thermodynamic property. THEOREM 1. If a relation exists among x, y, and z, then we may imagine z expressed as a function of x and y; whence, az (az dz = ax ay dx + M= (; If we let az az and N= ax ay then dz = M dx + N dy, where z, M, and N are all functions of x and y. Partially differentiating M with respect to y, and N with respect to x, we get (әм az an az and ду, дх ду дх, ду дх” Since the two second derivatives of the right-hand terms are equal, it follows that am ду an ax (10.30) This is known as the condition for an exact differential, and it applies to all four characteristic functions.