# 13.2: Compression

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The way in which the volume of a material decreases with pressure at constant temperature is described by the *isothermal* *compressibility*, κ:

\[ \kappa=-\frac{1}{V}\left(\frac{\partial V}{\partial P}\right)_{T}.\]

Note the necessary minus sign.

Later, we shall need to distinguish between “isothermal compressibility” and “adiabatic compressibility”, and we shall need a subscript to the symbol κ in order to distinguish between the two. For the time being, however, κ with no subscript will be taken to mean the isothermal compressibility.

The reciprocal of κ is called the isothermal *bulk* *modulus*, sometimes (understandably) called the isothermal *incompressibility*.

*Question*: What are the SI units for compressibility and bulk modulus?

*Exercise*: Show that the isothermal compressibility of an ideal gas is 1/*P*.

*Exercise*: What is the bulk modulus of air at atmospheric pressure?