The average speed of an ideal gas molecule at `27^(@)C` is `0.3 m, sec^(-1)`. The average speed at `927^(@)C`

Options

A. `0.3 ms^(-1)`
B. `0.6 ms^(-1)`
C. `1.2 ms^(-1)`
D. `2.4 ms^(-1)`

Explanation

`U_(av) = sqrt(((8RT)/(pi M)))`
Given `u_(av) = 0.3 m sec^(-1) ` at 300 K
`therefore u_(1) = 0.3 = sqrt((8R xx 300)/(pi M)) " " … (i)`
at T = 273 + 927 = 1200 K
`u_(2) = sqrt(((8 R xx 1200)/(pi M))) T " " … (ii)`
From (i) and (ii) , we get `(u_(2))/(0.3) = sqrt(((1200)/(300)))`
`therefore u_(2) = 0.6 sec^(-1)`