Question

Give relation between temperature coefficient of cell and entropy

Answer 1

According to Gibbs helmholtz equation ,
$\bold{\Delta{G}=\Delta{H}+T(\frac{\delta(\Delta{G})}{\delta{T}})_P}$
Here ∆G is Gibbs free energy , ∆H is heat ,T is temperature and $\bold{(\frac{\delta(\Delta{G})}{\delta{T}})_P}$ is rate of change of Gibbs free energy at constant pressure.

But we know, ∆G = -nEF
∴ $\bold{(\frac{\delta(\Delta{G})}{\delta{T}})_P}$ = -nF$\bold{(\frac{\delta{E}}{\delta{T}})_P}$
Put it in above equation,
Then, ∆G = ∆H - nFT$\bold{(\frac{\delta{E}}{\delta{T}})_P}$
Now, compare this equation with , ∆G = ∆H - T∆S,
Here ∆S is the entropy change.
Hence, ∆S = - nF$\bold{(\frac{\delta{E}}{\delta{T}})_P}[/Tex] [tex]\bold{(\frac{\delta{E}}{\delta{T}})_P}$,here is temperature coefficient and ∆S is entropy change.