Chapter 1, Problem 1.58E

Interpretation Introduction

Interpretation:

Two other forms of the cyclic rule in equation 1.26 is to be written using mnemonic in Figure 1.11.

Concept introduction:

Cyclic rule is a formula that relates partial derivatives of three interdependent variables. Notably, this rule can be stated in other names such as triple product rule, cyclic chain rule, Euler’s chain rule, cyclic relation. Intriguingly, this rule finds application in thermodynamics, where three variables can be interconnected frequently, by a function of the simple form $f(x,y,z)=0$. In this expression, each variable is given as an implicit function of other two variables. In an example, an equation of state for a fluid can be connected with temperature, volume and pressure in this relation.