Prove expansibility / isothermal compressibility

[Outrageous]

β is expansibility , (1/V)(∂V/∂T) at constant temperature
κ is isothermal compressibility , (-1/V)(∂V/∂P) at constant pressure

How to prove (∂P/∂T) at constant V = (β/κ)
Thank you

 

[Chestermiller]

β is expansibility , (1/V)(∂V/∂T) at constant temperature
κ is isothermal compressibility , (-1/V)(∂V/∂P) at constant pressure

How to prove (∂P/∂T) at constant V = (β/κ)
Thank you

dV = (∂V/∂T)_PdT + (∂V/∂P)_TdP

set dV = 0 to evaluate (∂P/∂T)_V

 

[Outrageous]

dV = (∂V/∂T)_PdT + (∂V/∂P)_TdP

set dV = 0 to evaluate (∂P/∂T)_V

Understand. Thank you