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Homework Help: Thermal Physics adiabatic and isothermal compressibilty

  1. Nov 24, 2013 #1
    Ok so I found something online but I need to understand this problem

    Prove that the ratio of the adiabatic compressibilty ks to the isothermal compressibility kr is equal to the ratio of the specific heat at constant colume, Cv, to that at constant pressure, Cp

    Definitions of the compressibility

    adiabatic compressibilty ks = (-1/v)(∂V/∂p)s

    isothermal compressibilty kT = (-1/V)(∂V/∂P)T

    I think we need to start with dS = (∂S/∂T)pdT + (∂s/∂p)TdP
  2. jcsd
  3. Nov 24, 2013 #2
    The isothermal compressibility can be obtained directly from the ideal gas law. The adiabatic compressibility can be obtained directly from PVγ=constant.
  4. Nov 24, 2013 #3
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