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JEE Advanced 2020 Paper 1

Section: Physics

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Question : 12 of 54

Marks: +1, -0

As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate

(\mathrm{KMnO}_4)

of different concentrations

n_1

n_2 (n_1 > n_2)

molecules per unit volume with

\Delta n = (n_1 - n_2) < < n_1 .

When they are connected by a tube of small length 1 and crosssectional area

S, \mathrm{KMnO}_4

starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force

-\beta v

on each molecule, where

\beta

is a constant. Neglecting all terms of the order

(\Delta n)^2,

which of the following is/are correct?

(k_B

is the Boltzmann constant)

[JEE Adv 2020 P1]

The force causing the molecules to move across the tube is $\Delta n k_B T S$
Force balance implies $n_1 \beta v l = \Delta n k_B T$
Total number of molecules going across the tube per sec is $\left( \frac{\Delta n}{l} \right) \left( \frac{k_B T}{\beta} \right) s$
Rate of molecules getting transferred through the tube does not change with time

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