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Properties of Matter question

2020 · Shift 1 · Q41
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Properties of Matter question

2020 · Shift 1 · Q41

JEE AdvancedPhysicsProperties of MatterMultiple correct+4 / −2
As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate (KMnO4) of different concentrations n1 and n2 (n1 > n2) molecules per unit volume with Δ\DeltaΔ n = (n1 − n2) << n1. When they are connected by a tube of small length l and cross-sectional area S, KMnO4 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 −β\betaβ v on each molecule, where β\betaβ is a constant. Neglecting all terms of the order (Δ\DeltaΔ n)2, which of the following is/are correct? (kB is the Boltzmann constant) JEE Advanced 2020 Paper 1 Offline Physics - Properties of Matter Question 33 English
  1. A
    the force causing the molecules to move across the tube is ΔnkbTS\Delta n{k_b}TSΔnkb​TS
  2. B
    force balance implies n1βvl=ΔnkBT{n_1}\beta vl = \Delta n{k_B}Tn1​βvl=ΔnkB​T
  3. C
    total number of molecules going across the tube per sec is (Δnl)(kBTβ)S\left( {{{\Delta n} \over l}} \right)\left( {{{{k_B}T} \over \beta }} \right)S(lΔn​)(βkB​T​)S
  4. D
    rate of molecules getting transferred through the tube does not change with time
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