The root mean square speed of gas molecules at a temperature `27K` and pressure 1.5 bar is `1 xx 10^(4) cm//sec` If both temperature and pressure are raised three times calculate the new rms speed of gas molecules .

Explanation

`P_(1) = 1.5 "bar", T = 27 K,`
`u_(rms) = 1 xx 10^(4) cm//sec`
(2) `P_(2) = 3 xx 5 1.5 "bar", T =27 xx 3K = 81k, u_(rms) =u_(2)`
`u_(rms) = sqrt((3RT)/(M))`
For 1: `1 xx 10^(4) == sqrt((3 xx 8.314 xx 10^(7) xx 27)/(M)) `
`M =67.34`
For 2: `= sqrt((3 xx 8.314 xx 10^(7) xx 27)/(67.34))`
` =1.73 xx 10^(4) cm//`sec .