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JEE Main 2018 · Molecular Speeds & Maxwell Distribution

Molecular Speeds & Maxwell Distribution question from JEE Main 2018

Q84JEE Main 2018Medium

Molecular Speeds & Maxwell Distribution

The mass of a hydrogen molecule is 3.32 ×\times 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45° to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on the wall is nearly:

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Answer: (a)

vv45°normalwallΔp = 2mv cos45°
  1. At 45∘45^\circ to the normal, only the normal component reverses: Δp=2mvcos⁡45∘\Delta p = 2mv\cos45^\circ per hit.
  2. Δp=2×3.32×10−27×103×0.707=4.69×10−24 kg m/s\Delta p = 2\times3.32\times10^{-27}\times10^3\times0.707 = 4.69\times10^{-24}\text{ kg m/s}
  3. P=n ΔpA=1023×4.69×10−242×10−4≈2.35×103 N m−2P = \frac{n\,\Delta p}{A} = \frac{10^{23}\times4.69\times10^{-24}}{2\times10^{-4}} \approx 2.35\times10^3\text{ N m}^{-2}
  4. So the answer is (a) 2.35×103 N m−22.35\times10^3\text{ N m}^{-2}.
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