To what temperature should the hydrogen at `327^(@)C` be cooled at constant pressure, so that the root mean square velocity of its molecules become half of its previous value?

Options

A. `-123^(@)C`
B. `123^(@)C`
C. `-100^(@)C`
D. `0^(@)C`

Answer

A

Explanation

The root mean square `v" rms"propsqrt((3RT)/(M))rArrTpropv_"rms"^(2)`
`rArr" " (T_(2))/(T_(1))=[(v_(2))/(v_(1))]^(2)=(1)/(4)`
`rArr" " T_(2)=(T_(1))/(4)=((227+327))/(4)`
=150 K = `-123^(@)C`