Dielectrics, heat capacity and polarization

[Kelsi_Jade]

Consider a dielecrtic with polarization P=(a+b/T)[itex]\epsilon[/itex] and heat capactiy C_{[itex]\epsilon[/itex]}=A+B[itex]\epsilon[/itex], where a and b are constants. Show that B=2bV/T² and find the isothermal dielectric constant [itex]\kappa[/itex]_el. Use properties of G(T,[itex]\epsilon[/itex])

I'm really not sure where to start with this one. Any help is apreciated to get going in the right direction.
I know εV_el/a
The only think I found in my notes is that C_{[itex]\epsilon[/itex]}=-T(∂²G/∂T²)_ε but I'm not sure how that plays into the question..

 

[NateD]

Since G(T,\epsilon) is the Gibbs energy of a system, we can use the definition of heat capacity to express it in terms of derivatives of G: C\epsilon= -T(∂2G/∂T2)ε From this, we can solve for B: B = -T(∂2G/∂T2)ε/\epsilon Substituting the given expression for P into the equation gives: B= (2bV)/T^2 To find the isothermal dielectric constant \kappael, we can use the definition of the dielectric constant: \kappael=P/E Therefore, \kappael=(a+b/T)/E