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Homework Help: Isothermal Compressibility: Derive an equation

  1. Oct 6, 2015 #1
    > 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. jcsd
  3. Oct 7, 2015 #2


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    It's often shown for n=1.
    Which derivative is useful for this problem?
  4. Oct 7, 2015 #3
    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?

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