JEE Advanced2020PhysicsMechanical Properties of FluidsActual
As shown schematically in the figure, two vessels contain water solutions (at temperature T ) of potassium permanganate KMnO 4 of different concentrations n 1 and n 2 n 1 > n 2 molecules per unit volume with Δ n = n 1 - n 2 ≪ n 1 . When they are connected by a tube of small length l and cross-sectional area S , KMnO 4 starts to diffuse from the left to the right vessel through the tube. Consider the collection of mol
Options
- Athe force causing the molecules to move across the tube is Δ n k B T S
- Bforce balance implies n 1 β v l = Δ n k B T
- Ctotal number of molecules going across the tube per sec is Δ n l k B T β S
- Drate of molecules getting transferred through the tube does not change with time
Correct answer
A. the force causing the molecules to move across the tube is Δ n k B T S
Step-by-step solution
(a) F = Δ P . A = P 1 - P 2 A = n 1 × RTA - n 2 RT . A F = Δ n R T A (b) β v × n 1 × A × ℓ = Δ n k B T A β v n 1 ℓ = Δ n k B T (c) dN dt = S v n 1 = s n 1 × Δ n k B T β n 1 ℓ = S × Δ n k B T S β ℓ (d) Δ n → decreasing then d N d t → decreasing