UPSC Civil Services (Mains), Chemistry optional · 2018 · Paper I

Q2(b)(ii). Effect of temperature on viscosity

Question

Discuss the effect of temperature on the viscosity of liquids and gases.

The viscosity of a liquid falls on heating (η∝ e^(Eₐ/RT)); the viscosity of a gas rises on heating (η∝ T^(1/2)).

a molecule can move only when it gains enough energy Eₐ to escape the cage of its neighbours. The fraction of such molecules grows as e^(-Eₐ/RT), so the mobility rises and η∝ e^(+Eₐ/RT) (note the positive exponent).
The viscosity of a liquid therefore falls sharply on heating; a plot of η against 1/T is nearly linear. Water: 0.891 mPa s at 298 K; between 0 and 100°C its viscosity falls to about one-sixth. In water the breaking of hydrogen…
viscosity comes from molecules carrying momentum from one layer to the next. Kinetic theory gives η=13 m; λ N is constant, so η is independent of pressure and η∝ T^(1/2).
The viscosity of a gas therefore rises on heating: faster molecules carry more momentum across.

The full model answer

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

Liquids: a molecule can move only when it gains enough energy Eₐ to escape the cage of its neighbours. The fraction of such molecules grows as e^(-Eₐ/RT), so the mobility rises and η∝ e^(+Eₐ/RT) (note the positive exponent).
The viscosity of a liquid therefore falls sharply on heating; a plot of η against 1/T is nearly linear. Water: 0.891 mPa s at 298 K; between 0 and 100°C its viscosity falls to about one-sixth. In water the breaking of hydrogen bonds adds to the effect.
Gases: viscosity comes from molecules carrying momentum from one layer to the next. Kinetic theory gives η=13 m; λ N is constant, so η is independent of pressure and η∝ T^(1/2).
The viscosity of a gas therefore rises on heating: faster molecules carry more momentum across.
The opposite trends show that viscosity has different origins: intermolecular attraction in a liquid, molecular motion in a gas.

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