Show $\bigg(\frac{\partial x}{\partial y}\bigg) \bigg(\frac{\partial y}{\partial z}\bigg)\bigg(\frac{\partial z}{\partial x}\bigg) = - 1,$
Prove that $\frac{\partial x}{\partial y} \frac{\partial y}{\partial z} \frac{\partial z}{\partial x} = -1$ and verify ideal gas law