Differentiation of compression factor

[yungwun22]

Homework Statement

The problem reduces the derivative (dZ/d(1/V)) to (dZ/dV) x (dV/d(1/V)), where Z is the compression factor and v is molar volume. It further shows that it equals -V^2(dZ/dV). I don't know how they arrived at that value because by my logic it should be 1/(-V^2).

Homework Equations

The Attempt at a Solution

 

[gabbagabbahey]

A simple substitution of the form u=1/V should be enough to prove to you that dV/(d(1/V))=-V^2.

 

[Blueshift5]

The differentiation of the compression factor involves using the chain rule, where the derivative of Z with respect to V is multiplied by the derivative of V with respect to (1/V). This is because the variable V is in the denominator of the expression for Z.

As for the resulting value of -V^2(dZ/dV), this can be derived using the quotient rule and simplifying the expression. It is also possible that there may be a typo in the original problem, as you mentioned that your logic suggests it should be 1/(-V^2). I would recommend double checking your work and the given problem to ensure accuracy.