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Isothermal and Adiabatic Compressibility

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Could you please show me how to do the problem attached? Thank you.

The isothermal compressibility K_T and the adiabatic compressibility K_S are defined by

K_T = - 1/V(derivative V derivative p)_T and K_S = - 1/V (derivative V derivative p)_s,

where the symbolbs have their usual meanings. Show that K_S/K_p = 1/ gamma where gamma is the ratio of principal specific heats.

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In this response, the relation between isothermal and adiabatic compressibility of a gas is derived. The solution has been provided in an attached Word document with all calculations and steps show in a very detailed manner.

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