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Kinetic Theory of Gases and Radiation — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsKinetic Theory of Gases and Radiation4 Marks
Question
At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively)
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Answer

Data: $T_2=273 K , M_{01}$ (oxygen) $=32 \times 10^{-3} kg / mol , M_{02}$ (hydrogen) $=4 \times 10^{-3} kg / mol$ The rms speed of oxygen molecules, $v _1=\sqrt{\frac{3 R T_1}{M_{01}}}$ and that of helium molecules, $v _2=$ $\sqrt{\frac{3 R T_2}{M_{02}}}$
When $v _1= v _2$
$
\sqrt{\frac{3 R T_1}{M_{01}}}=\sqrt{\frac{3 R T_2}{M_{02}}}
$
$\therefore \frac{T_1}{M_{01}}=\frac{T_2}{M_{02}}$
$\therefore$ Temperature, $\begin{aligned} T_1 & =\frac{M_{01}}{M_{02}} \cdot T_2=\frac{\left(32 \times 10^{-3}\right)(273)}{4 \times 10^{-3}} \\ & =2184 K \end{aligned}$

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