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You are given the following group of par...

You are given the following group of particles, `n_i` represents the number of molecules with speed `v_i`
`n_(i)" 2 4 8 6 3"`
`V_i(ms^(-1))" 1.0 2.0 3.0 4.0 5.0"`
Calculate (i) average speed (ii) rms speed (iii) most probable speed.

Text Solution

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(i) average speed `V_(ang)=(n_(1)v_(1)+n_(2)v_(2)+n_(3)v_(3)+n_(4)v_(5)+n_(5)v_(5))/((n_(1)+n_(2)+n_(3)+n_(4)+n_(5))`
`=((2 xx 1)+(4 xx 2)+(8 xx 3)+(6 xx 4)+(3 xx 5))/((2+4+8+6+3))`
`=(73)/(23)=3.17 ms^(-1)`
(ii) root mena square speed is
`v_(rms) =((n_(1)v_1^2+n_2v_2^2+n_3v_3^2+n_4v_4^2+n_5v_5^2)/(n_1+n_2+n_3+n_4+n_5))^(1//2)`
`=((2 xx 1+4 xx 4+8 xx 9 +6 xx 16 +3 xx 25)/(2+4+8+6+3))^(1//2)=3.36ms^(-1)`
(ii) Most probable speed 3m/s by which largest molecules are moving at any time.
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