Additional Useful Relations Between Partial Derivatives

Additional Useful Relations Between Partial Derivatives 

It is fairly common in thermod5mamics to have measured values for some partial derivative such as (9///97 )p, , which is equal to the heat capacity at constant pressure. However, some other partial derivatives are difficult or impossible to measure. It is convenient to be able to express such partial derivatives in terms of measurable quantities. We now obtain some identities that can be used for this purpose. 

The next identity is the reciprocal identity, which states that a derivative is equal to the reciprocal of the derivative with the roles of dependent and independent variables reversed  

The same variables must be held constant in the two derivatives. 

There are two kinds of second partial derivatives. If z = z x, y) we can differentiate twice with respect to x  

---

Additional Useful Relations Between Partial Derivatives... 

---