Question
The root mean square velocity of molecules in a sample of helium is `5/7`th that of the molecules in a sample of hydrogen. If the temperature of hydrogen sample is `0^circ C` . Then the temperature of helium sample is about :
Answer: Option C
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From the relation , `v_(rms)` =` sqrt((3R)/(m))`
or `(v_(rms)He)/(v_(rms) H_2)` = `sqrt(T_1/m_1 xx m_2/T_2)`
or `5/7 = sqrt((T_1 xx 2)/(4 xx (0 + 273)))`
or `(5/7)^2 = (T_1)/(2(273))`
or `T_1 = (546 xx 25)/(49)`
= 278.6 K
Hence , `T_1 = 5.6^circ C`
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