- #1
mmedrano8
- 9
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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
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