The discussion focuses on proving the relationship between expansibility (β) and isothermal compressibility (κ) in thermodynamics, specifically demonstrating that (∂P/∂T) at constant volume equals (β/κ). Expansibility is defined as (1/V)(∂V/∂T) at constant temperature, while isothermal compressibility is defined as (-1/V)(∂V/∂P) at constant pressure. The proof involves manipulating the differential volume equation, dV = (∂V/∂T)PdT + (∂V/∂P)TdP, and setting dV to zero to isolate (∂P/∂T) at constant volume.
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Outrageous said: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 said:dV = (∂V/∂T)PdT + (∂V/∂P)TdP
set dV = 0 to evaluate (∂P/∂T)V