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Two gases A and B are contained in two separate, but otherwise identical containers. Gas A consists of monoatomic molecules, each with atomic mass of 4 u whereas, Gas B consists of rigid diatomic molecules, each with atomic mass of 20 u. If Gas A is kept at $30^{0} C$ , at what temperature should Gas B be kept so that both have the same r.m.s. speed?

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$30^{0} C$

$54^{0} C$

$300^{0} C$

$627^{0} C$

answer is C.

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Detailed Solution

$V_{r m s} = \sqrt{\frac{3 R T}{M}}$

$V_{A} = V_{B}$

$\frac{T_{1}}{M_{1}} = \frac{T_{2}}{M_{2}}$

$\frac{30}{4} = \frac{T_{2}}{2 (20)} T_{2} = 300^{0} C$

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