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The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times. As a result, the diffusion coefficient of this gas increases x times. The value of x is

Correct answer

4

Step-by-step solution

Diffusion coefficient ∝ mean free path × mean speed D ∝ i ̄ × c ̄ But i ̄ = 1 2 π σ 2 R T P N 0 or i ̄ ∝ T P and c ̄ = 8 R T π M or c ̄ ∝ T M So D ∝ T P . T M or D ∝ T 3 2 P M or D 1 D 2 = T 4 T 3 2 2 P P = 1 4 3 2 × 2 = 1 2 3 × 2 = 1 4 or D 2 = 4 D 1

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