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KVPY2017PhysicsKinetic Theory of Gases

The number of gas molecules striking per second per square meter of the top surface of a table placed in a room at 20^ C and 1 atmospheric pressure is of the order of ( k _ B =1.4 10⁻²³ ~J / K . , and the average mass of an air molecules is 5 10⁻²⁷ ~kg )

Options

  1. A10²⁷
  2. B10²³
  3. C10²⁵
  4. D10²⁹

Correct answer

A. 10²⁷

Step-by-step solution

V _ rms = 3 RT M = 3 kT M ₀ P = N 2 mV _ rms 1.01 10⁵= N 2 5 10⁻²⁷ V _ rms aligned N &= 1.01 10⁵ 5 10⁻²⁷ 2 5 10⁻²⁷ 3 1.4 10⁻²³ 293 &=6.43 10²⁷ aligned

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