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UPSC Combined Geo-Scientist

Chemist

  • 3 descriptive papers
  • 200 marks each
  • 3 h per paper

Mains Paper II covers physical chemistry.

UPSC Combined Geo-Scientist, Mains · 2017 · Mains Paper II

Q1(d). Carnot efficiency

Question

List the factors influencing Carnot-engine efficiency and explain their effects.

Answer in brief

η=1-Tc/Tₕ: efficiency increases with a hotter source or a colder sink, using absolute temperatures.

Key points

  • For a reversible engine, η=W/Qₕ=1-|Qc|/Qₕ. Entropy balance over a Carnot cycle gives Qₕ/Tₕ=|Qc|/Tc.
  • Hence only the reservoir temperatures determine the maximum efficiency. At fixed Tc, ∂η/∂ Tₕ=Tc/Tₕ²>0; at fixed Tₕ, ∂η/∂ Tc=-1/Tₕ<0.
  • Efficiency is independent of the working substance for a reversible Carnot engine.
  • Friction, heat leakage and finite temperature differences reduce the efficiency of an actual engine below the Carnot limit.

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.

Model answer to Q1(d), 2017 Mains Paper II: solution pages 3 and 4
Solution pages 3 and 4 of 19
Read the whole 2017 solution2017 question paper

CoversCarnot efficiencyHeat engines

All parts of Question 1