Question

1. Maxwell Relations In class, using the exactness of the Helmholtz free energy, we derived one of the Maxwell relations, \left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial P}{\partial T}\right)_V. Now, let us derive another Maxwell relation: the Gibbs free energy is defined as, G = F + PV. a) Show that dG = -SdT + VdP. b) Using the result from part a), prove that $-\left(\frac{\partial S}{\partial P}\right)_T = \left(\frac{\partial V}{\partial T}\right)_P.$

          1. Maxwell Relations
In class, using the exactness of the Helmholtz free energy, we derived one of the Maxwell
relations, \left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial P}{\partial T}\right)_V.
Now, let us derive another Maxwell relation: the Gibbs free energy is defined as, G = F + PV.
a) Show that dG = -SdT + VdP.
b) Using the result from part a), prove that $-\left(\frac{\partial S}{\partial P}\right)_T = \left(\frac{\partial V}{\partial T}\right)_P.$

1. Maxwell Relations
In class, using the exactness of the Helmholtz free energy, we derived one of the Maxwell
relations, ((∂S)/(∂V))T = ((∂P)/(∂T))V.
Now, let us derive another Maxwell relation: the Gibbs free energy is defined as, G = F + PV.
a) Show that dG = -SdT + VdP.
b) Using the result from part a), prove that -((∂ S)/(∂ P))T = ((∂ V)/(∂ T))P.

Added by Lu-S H.

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