drive ∆ G=-T∆S from the
total
relationship G=H-TS
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Answer:
G=H−TS
on differentiating
ΔG=ΔH−T(ΔS)−(ΔT)S
the r×n occurs at constant temperature, ΔT=0
ΔG=ΔH−T(ΔS)⟶(1)
We also know that entropy change of surroundings.
ΔS
surrounding
=
T
−ΔH
ΔH=−T(ΔS)
surr
⟶(2)
Substituting (2) in (1)
ΔG=−T.ΔS
surr
−TΔS
ΔG=−T(ΔS
surr
+ΔS)
we know, (ΔS
surr
+ΔS)=ΔS
total
⇒ΔG=−T(ΔS)
total
Thus, the relationship ΔG=−T(ΔS)
total
is derived
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