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At `27^(@)C` a gas contains 10 molecules travelling with a speed of 4 `ms^(-1)`, 20 molecules travelling with a speed of 5 m `s^(-1)` and 40 molecules travelling with a speed of 8 m `s^(-1)`. Calculate the average speed, root mean square speed and most probable speed of the gas at `27^(@)C`. |
Answer» Average speed `(overset(bar)(c )=(sumn_(i)v_(i))/(sumn_(i))=(10xx4+20xx5+40xx8)/(10+20+40)=(460)70)` `=6.56 m s^(-1)` Root mean square speed (c )`=sqrt((sumn_(i)v_(i))/(sumn_(i)))=sqrt((10xx4^(2)+20xx5^(2)+40xx82)/(10+20+40))` `=sqrt((160+500+2560)/(70))=6.678 m s^(-1)` Most probable speed `(c^(**))=0.816xxc=0.816xx6.78 m s^(-1)=5.53 m s^(-1)`. |
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