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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 · 2024 · Paper I

Q3(b)(ii). Pressure difference across a water droplet of radius 150 nm

5 marks
Topic: Liquid state
Answered

Question

Calculate the difference in pressure across the liquid–air interface for a water droplet of radius 150 nm.

Answer in brief

Δp = 2γ/r = 9.6 × 10⁵ Pa (9.5 atm), higher inside the droplet.

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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.

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Read the whole 2024 solution 2024 question paper

Topic notes: the liquid state: surface tension, the Kelvin equation, capillary action, viscosity and liquid crystals, with every Civil Services, IFoS and Geo-Scientist PYQ →

CoversLaplace equationsurface tensionpressure inside a dropletKelvin equationcurved surface

All parts of Question 3

3(a)(i) Viscosity of air at 298 K and at 0 K10 marks
3(a)(ii) Boyle temperature of Ar, CH₄ and C₆H₆5 marks
3(b)(i) Surface tension: ethanol or dimethyl ether5 marks
3(b)(ii) Pressure difference across a water droplet of radius 150 nm5 marks
3(c)(i) Change in Helmholtz energy on reversible isothermal compression10 marks
3(c)(ii) Why a tyre gets hot when it is pumped5 marks
3(c)(iii) Pressure of O₂ over NiO at 25 °C5 marks
3(c)(iv) Final temperature after Joule–Thomson expansion5 marks