For two gases, A and B with molecular weights M A and M B , it is observed that at a certain temperature, T, the mean velocity of A is equal to the root mean square velocity of B. Thus the mean veloci

Question

For two gases, A and B with molecular weights M A and M B , it is observed that at a certain temperature, T, the mean velocity of A is equal to the root mean square velocity of B. Thus the mean velocity of A can be made equal to the mean velocity of B, if

TestHub · Accepted Answer

Given √(8RT/π M A ) = √(3RT/M B ) ⇒ M B = (3π)/8M A ≈ 1.18 M A , so M B > M A . Equal mean velocities require √(T A /M A ) = √(T B /M B ), i.e. T B /T A = M B /M A > 1, so B must be hotter than A. Starting from both at T, lower A to T' < T while keeping B at T; then T/T' = M B /M A can be satisfied. Confirms Ans (b).

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