Partial Derivatives and Gas Laws

Equations of state deal with many variables. The total derivative of a function of multiple variables, F x, y,z.), is defined as 

In equation 1.12, we are taking the derivative of the function F with respect to one variable at a time. In each case, the other variables are held constant. Thus, in the first term, the derivative 

FIGURE 1.5 (a) Definition of slope for a straight line. The slope is the same at every point on the line, (b) A curved line also has a slope, but it changes from point to point. The slope of the line at any particular point is determined by the derivative of the equation for the line. 

Unless otherwise noted, all art on this page is Cengage Learning 2014. 

Using equations of state, we can take derivatives and determine expressions for how one state variable changes with respect to another. Sometimes these derivatives lead to important conclusions about the relationships between the state variables, and this can be a powerful technique in working with thermodynamics. 

---