JEE Main 2023 · 13 April · morning · Single correct · +4 / −1

The rms speed of oxygen molecule in a vessel at particular temperature is (1+5/x)^(1/2) v, where v is the average speed of the molecule. The value of x will be:
( Take π=22/7)

  1. (a) 4
  2. (b) 8
  3. (c) 28
  4. (d) 27
Answer and solution

Answer (c) 28

Solution

Physics sir · 4 steps

Square the ratio of rms speed to average speed; the gas and the temperature both cancel out.

  1. Write both speeds. For a gas of molar mass M at temperature T, vᵣₘₛ = √(3RT/M) and v_(avg) = √(8RT/(π M)).
  2. Take the ratio. Divide one by the other and square. R, T and M all cancel, so the result is the same for oxygen or any other gas.

    (vᵣₘₛ/v_(avg))² = 3π/8 = (3 × 22)/(7 × 8) = 66/56 = 33/28

  3. Match the form. The question gives (vᵣₘₛ/v)² = 1 + 5/x. Write 33/28 = 1 + 5/28.
  4. So. Comparing the two forms gives x = 28, which is option (c).

The idea to keep. Speed ratios in kinetic theory are pure numbers: vᵣₘₛ : v_(avg) : vₘₚ = √3 : √(8/π) : √2. Learn this ratio once and every such question becomes a fraction exercise.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Kinetic Theory of Gases

Asked about 130 times in JEE Main since 2020. This question is from 2023.