# Isothermal Compressibility: Derive an equation

1. Oct 6, 2015

### johnr

> The isothermal compressibility $\kappa_t$ of a substance is defined as $$\kappa_t = -\frac{1}{V} \left ( \frac{\partial V}{\partial P} \right )_T$$ Obtain an expression for the isothermal compressibility of an ideal gas. (PV = RT) in terms of p.

I believe that the ideal gas law equation may be a typo (i.e. PV = nRT). Anyways, I have first set $P = RT/V$ and then taken $P_{VT}$ (partial derivatives). Is this the right way to go?

2. Oct 7, 2015

### Bystander

It's often shown for n=1.
Which derivative is useful for this problem?

3. Oct 7, 2015

### Staff: Mentor

It doesn't matter whether you use PV=nRT or PV=RT. You get the same answer either way. So solve for V and take the partial derivative with respect to P at constant T (and n). What do you get?

Chet