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Question
Consider an ideal gas with following distribution of speeds.
| Speed (m/s) | % of molecules |
| 20 | 10 |
| 400 | 20 |
| 600 | 40 |
| 800 | 20 |
| 1000 | 10 |
If all the molecules with speed 1000 m/s escape from the system, calculate new Vrms and hence T.
Solution
When molecules escape 1000 ms–1 out then,
`v_(rms)^2 = (10 xx (200)^2 + 20 xx (400)^2 + 40 xx (600)^2 + 20 xx (800)^2)/(10 + 20 + 40 + 20)`
`v_(rms)^2 = (10^5 [4 + 32 + 144 + 128])/90`
`v_(rms) = sqrt((10^5[308])/90)`
= `sqrt(10^4/9 xx 308`
= `100/3 sqrt(308)`
= `33.33 xx 17.55 ≅ 582 ms^-1`
`T = 1/3 (mv_(rms)^2)/K_B`
= `(3 xx 10^-26 xx (585)^2)/(3 xx 1.38 xx 10^-23)`
= `(585)^2/138 xx 10^(-24 + 23)`
`T = 4.24 xx 10^-1 xx 585`
= 248.04 K
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