(a) Using the functional relationships $z = z(x, y)$ and $x = x(y, z)$, derive the reciprocity and
cyclic relations
$\left(\frac{\partial x}{\partial y}\right)_z \left(\frac{\partial y}{\partial x}\right)_z = 1$
$\left(\frac{\partial y}{\partial z}\right)_x \left(\frac{\partial z}{\partial x}\right)_y \left(\frac{\partial x}{\partial y}\right)_z = -1$
Start by taking the differential of the two functional relationships and be sure to show all
your work.
(b) Using the ideal gas equation of state, verify the
(a) reciprocity relation
(b) cyclic relation
at constant $p$.
