Expansion of an Incompressible Body

If we apply pressure to an incompressible body in the course of an adiabatic process, the body may unexpectedly expand. The increase of pressure leaves even an incompressible body literally not cool. The body can accept energy and can warm up when thermally isolated. Since the pressure has no effect on the dimensions, but the temperature has effect, the body may expand on heating. 

More precisely we must differentiate between an adiabatically incompressible boy and an isothermally incompressible body. Since the generalized susceptibilities must be positive for the sake of stability of matter, we have 

Here the dependent variables of the volume must be extensive. On the other hand, 

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