# Formulas for compressibility of solids

I am taking a course in mechanics this semester, as well as a course in reservoir physics. Both courses have sections devoted to pressure/compressibility of solids, but the formulas look slightly different, so I wondered if they really mean the same or not.

In my mechanics class I am told that:

$$\Delta P = B \left(\frac{- \Delta V}{V_0}\right)$$

Where $B$ is a constant known as the bulk modulus of a given material.

In my reservoir physics class I am presented with the formula:

$$c = -\frac{1}{V} \left(\frac{\partial V}{\partial p}\right)_{T}$$

Where $c$ is referred to as isothermal compressibility.

So my question is - are these formulas basically the same, where $c = \frac{1}{B}$? And if they are not the same, can someone please explain the difference to me? I would really appreciate if someone could help me with this!

Yes, the bulk modulus $B$ is the inverse of the isothermal compressibility $c$, $$B = \frac {1}{c}.$$ See e.g. Wikipedia.