When temp coefficient of emf of cell reaction is zero them
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we know, ∆G = -nFE
From the Gibbs-Helmholtz equation,
∆G = ∆H + T(dG/dT)
Now putting,G = -nFE in above equation,
∆G = ∆H + T(d(-nFE)/dT))
∆G = ∆H - nFT (dE/dT)
But given temperature coefficient of emf cell reaction is zero, I.e., dE/dT = 0
So, ∆G = ∆H - nFT × 0 = ∆H
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