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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 · 2017 · Paper I

Q2(a)(i). Viscosity coefficient: dimension, SI unit, and its rise with T in a gas

  • 10 marks
  • Answered
Question

What is the dimension of viscosity co-efficient? What is its unit in SI system? The temperature effect on viscosity co-efficient of ideal gas is positive. Explain.

Answer in brief

[η]=M L⁻¹ T⁻¹; SI unit kg m⁻¹ s⁻¹ = Pa s. For a gas η=13 mλ c N is independent of pressure and grows as c∝√T, so η increases with temperature.

Key points

  • Definition. Between two layers moving with a velocity gradient dv/dz, the tangential force per unit area is F/A=η (dv/dz) (Newton's law); η is the coefficient of viscosity.
  • Dimension: η=(F/A)/(dv/dz)=M L T⁻²/L²L T⁻¹/L, [η]=M L⁻¹ T⁻¹
  • kg m⁻¹ s⁻¹=N s m⁻²=Pa s. The cgs unit is the poise: 1 P = 0.1 Pa s.
  • Origin in a gas. Molecules cross from a fast layer to a slow one and carry momentum with them; the slow layer is speeded up and the fast layer slowed. Kinetic theory gives η=13 mλ c N (N = number density, λ = mean distance…

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

  1. Definition. Between two layers moving with a velocity gradient dv/dz, the tangential force per unit area is F/A=η (dv/dz) (Newton's law); η is the coefficient of viscosity.
  2. Dimension: η=(F/A)/(dv/dz)=M L T⁻²/L²L T⁻¹/L, [η]=M L⁻¹ T⁻¹
  3. SI unit: kg m⁻¹ s⁻¹=N s m⁻²=Pa s. The cgs unit is the poise: 1 P = 0.1 Pa s.
  4. Origin in a gas. Molecules cross from a fast layer to a slow one and carry momentum with them; the slow layer is speeded up and the fast layer slowed. Kinetic theory gives η=13 mλ c N (N = number density, λ = mean distance between collisions).
  5. No pressure effect: λ=1/σN, so λN=1/σ and η=m c/3σ. More molecules carry momentum, but each carries it a shorter distance.
  6. Rise with T: c=√(8k_BT/π m), so η=(1)/(3σ)√((8mk_BT)/(π))∝√T. At higher T molecules move faster and carry momentum across the layers more often, so the gas becomes more viscous.
  7. Data: argon 210 μP at 273 K and 223 μP at 293 K; air 173 and 182 μP. Real gases rise a little faster than √T because σ falls slightly as T rises.
  8. Contrast: a liquid becomes less viscous on heating, η∝ e^(Eₐ/RT): molecules must escape from their neighbours, and heating helps them do so.

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Model answer to Q2(a)(i), 2017 Paper I: solution page 7
Solution page 7 of 38
Read the whole 2017 solution2017 question paper

All parts of Question 2