Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 7.4-2

STABILITY OF THERMODYNAMIC SYSTEMS

Physics — Statistical Mechanics · adiabatic-bulk-modulus

Problem

The adiabatic bulk modulus is defined by βS=−v(∂P∂v)s=−V(∂P∂V)S,N\beta_S = -v\left(\frac{\partial P}{\partial v}\right)_s = -V\left(\frac{\partial P}{\partial V}\right)_{S,N} Express this quantity in terms of cpc_p, cvc_v, α\alpha, and κT\kappa_T (do not eliminate cpc_p). What is the relation of your result to the identity κs/κT=cv/cp\kappa_s/\kappa_T = c_v/c_p (recall Problem 3.9-5)?

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