Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 7.2-1

MAXWELL RELATIONS

Physics — Statistical Mechanics · maxwell-relations-heat-transfer

Problem

In the immediate vicinity of the state T0,v0T_0, v_0 the volume of a particular system of 1 mole is observed to vary according to the relationship v=v0+a(T−T0)+b(P−P0)v = v_0 + a(T - T_0) + b(P - P_0) Calculate the transfer of heat dQdQ to the system if the molar volume is changed by a small increment dv=v−v0dv = v - v_0 at constant temperature T0T_0. Answer: dQ=T(∂S∂V)TdV=T(∂P∂T)VdV=−aTb dVdQ = T\left(\frac{\partial S}{\partial V}\right)_T dV = T\left(\frac{\partial P}{\partial T}\right)_V dV = -\frac{aT}{b}\,dV

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