Chapter 15.4, Problem 69E

The Ideal Gas Law The pressure, temperature, and volume of an ideal gas are related by PV = kT, where k > 0 is a constant. Any two of the variables may be considered independent, which determines the dependent variable.

a. Use implicit differentiation to compute the partial derivatives $\frac{\partial P}{\partial V},\frac{\partial T}{\partial P}$,and $\frac{\partial V}{\partial T}$.

b. Show that $\frac{\partial P}{\partial V}\frac{\partial T}{\partial P}$ $\frac{\partial V}{\partial T}$ = −1 (See Exercise 75 for a generalization.)