2. Gibbs free energy question: Express the differential of its Gibbs free energy

Question

2. Gibbs free energy question: Express the differential of its Gibbs free energy dG in terms of dT and dV. The heat capacity, isothermal compressibility, and thermal expansion coefficient should be in the answer.

A closed system is described by state variables: temperature T, entropy S, pressure P and volume V. Express the differential of its Gibbs free energy dG in terms of dT and dV. The expression may contain state variables T, P, V and measurable quantities including volumetric thermal expansion coefficient alphav = ( V / T)P/V, isothermal compressibility betaT = -( V / P)T / V, and heat capacity Cp. Useful mathematical relation: ( x/ y)z ( y/ z)x ( z/ x)y = -1

Explanation / Answer

Gibbbs free energy is given as

            G = H-TS

      Here H = Enthalpy of reaction, T = Temprature and S = entropy and G = Gibbs free energy

            G = P dV - sdT..............1

         ( dG / dT)p = -S

          Putting the value of -S in equation 1

             G = H - T( dG/dT)p

              G/T = H/T - (dG/dT)p

                d/dT (G/T) = -G / T2 + 1/T (dG/dT)p

                  ( d/dT ( G/T) )P = 1/T ( -G/T + (dG/dT)p )

                    d / dt(G/T)p = -H /T2

       Differentiaiton with respect to volume

                 We know that

               G = A + PV             ( Here A is Helmoltz free energy = U - TS)

               G = U - TS + PV

           Differentiating with respect to VOlume

               dG = dA + d(PV)

               dG = dA + PdV + VdP

               For constant prasure

             dG = dA + pdV +0

            (dG /dV)p =d /dV(U - TS) + P

                   (dG /dV)p = dU/dV - T dS/dV - SdT/dV + P

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.