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

`v_(rms) prop sqrt((3RT)/(M))`
`implies T prop v_(rms)^(2)`
`implies (T_(2))/(T_(1))=[(v_(2))/(v_(1))]^(2)=(1)/(4)`
`implies T_(2)=(T_(1))/(4)=((273+327))/(4)`
`=150 K=- 123^(@)C`