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  • Let A and B be two gases and given : <img alt="\mathrm{\frac{T_{A}}{M_{A}}=4 \cdot \frac{T_{B}}{M_{B}}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfrac%7BT_%7BA%7D%7D%7BM_

Let A and B be two gases and given : \mathrm{\frac{T_{A}}{M_{A}}=4 \cdot \frac{T_{B}}{M_{B}}}, where, \mathrm{T} is the temperature and \mathrm{M} is molecular mass. If \mathrm{C_{A}} and \mathrm{C_{B}} are the rms speed, then the ratio \mathrm{\frac{C_{A}}{C_{B}}} will be equal to

Option: 1

2


Option: 2

4


Option: 3

1


Option: 4

0.5


Answers (1)

best_answer

\mathrm{\frac{T_{A}}{M_{A}}=4 \frac{T_{B}}{M_{B}}}


\mathrm{\Rightarrow \quad \sqrt{\frac{T_{A}}{M_{A}}}=2 \sqrt{\frac{T_{B}}{M_{B}}}}

\mathrm{\Rightarrow \quad \sqrt{\frac{3 R T_{A}}{M_{A}}}=2 \sqrt{\frac{3 R T}{M_{B}}}
\mathrm{\Rightarrow \quad C_{A}=2 C_{B}}
\mathrm{\Rightarrow \quad \frac{C_{A}}{C_{B}}=2}

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