UPSC Combined Geo-Scientist, Mains · 2025 · Mains Paper II
Q1(e). Fall of G with temperature at constant pressure
Question
For a closed system, at constant pressure, Gibbs free energy (G) decreases with increase of temperature and vice versa. Justify with reasons.
Answer in brief
(∂G/∂T)P = −S and S is always positive, so G falls as T rises and rises as T falls.
Key points
- G = H − TS ⇒ dG = V dP − S dT (closed system, only PV work) ⇒ (∂G/∂T)P = −S.
- Third law: S > 0 for every substance above 0 K ⇒ the slope is always negative.
- S(gas) > S(liquid) > S(solid) ⇒ G of the gas falls fastest.
- Curvature: (∂²G/∂T²)P = −CP/T < 0 ⇒ each curve is concave downwards.
- Vice versa: lowering T raises G along the same curve.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
CoversGibbs free energytemperature dependence of G(∂G/∂T)P = −Sentropythird law
All parts of Question 1
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