Two gases A & B are kept in a container having molecular weight M A & M B respectively. At a certain temperature ' T ' the U avg of ' A ' is equal to the U rms of ' B &#

Question

Two gases A & B are kept in a container having molecular weight M A ​ & M B ​ respectively. At a certain temperature ' T ' the U avg of ' A ' is equal to the U rms ​ of ' B '. Then select the correct option. [ T A ​ & T B ​ are temperature of A & B]

TestHub · Accepted Answer

Question Explanation: Comparing different molecular speed types for two gases. Concept: Molecular Speed Relationships

Solution: By equating the formulas for average speed and root mean square speed, the relationship between molecular weights is established.

$U_{a r g (A)} = \frac{8 RT}{π M _{A}}$ and $U_{r m s (B)} = \frac{3 RT}{M _{B}}$

$\frac{8 RT}{π M _{A}} = \frac{3 RT}{M _{B}}$

⇒ $M_{B} = \frac{3 π}{8} . M_{A}$

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