VKC ScienceChemistry for written exams Telegram

UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2021 · Paper I

Q1(c). Rubber band: change of length on heating

Question

For a rubber band (∂T/∂l)S = −(T/CV)(∂S/∂l)T. What would be the length of the rubber band with an increase in temperature? Explain it.

Answer in brief

A stretched rubber band (one that carries a load) shortens on heating, (∂l/∂T)f < 0, because stretching lowers its entropy and heat pulls the chains back towards the coiled state.

Key points

  • Stretching draws the polymer chains out along the pull, so fewer shapes remain: (∂S/∂l)T < 0, and the relation gives (∂T/∂l)S > 0.
  • A band stretched quickly turns warm and cools again on release.
  • The Maxwell relation (∂S/∂l)T = −(∂f/∂T)l shows that a band held at fixed length pulls harder when hot.
  • The cyclic rule gives (∂l/∂T)f < 0: under a fixed load the length decreases as the temperature rises.
  • For rubber (∂U/∂l)T ≈ 0, so f = −T(∂S/∂l)T: the restoring force is entropic and proportional to T (Gough–Joule effect).

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(c), 2021 Paper I: solution pages 5 and 6
Solution pages 5 and 6 of 59
Read the whole 2021 solution2021 question paper

Topic notes: the second and third laws, entropy, Gibbs energy and Maxwell relations, with every Civil Services, IFoS and Geo-Scientist PYQ →

Coversrubber elasticityentropic forceMaxwell relationGough–Joule effectthermodynamics of rubber band

All parts of Question 1