Five molecules of a gas have speed `2, 4, 6, 8 km//s`. Calculate average speed. Rms speed and most probable speed of these molecules.

Explanation

Here, `upsilon_(1) = 2km//s, upsilon_(2) = 4 km//s`,
`upsilon_(3) = 4 km//s, upsilon_(4)= 6km//s, upsilon_(5)=8 km//s`
`C_(av) = (upsilon_(1)+upsilon_(2)+upsilon_(3)+upsilon_(4)+upsilon_(5))/(5)`
`=(2+4+4+6+8)/(5) = 24/5 = 4.8 m//s`
`C_(rms) = sqrt((upsilon_(1)^(2)+upsilon_(2)^(2)+upsilon_(3)^(2)+upsilon_(4)^(2)+upsilon_(5)^(2))/(5))`
`= sqrt((2^(2)+4^(2)+4^(2)+6^(2)+8^(2))/(5))`
`= sqrt((4+16+16+36+64)/(5))`
`C_(rms) = sqrt((136)/(5)) = sqrt(27.2) = 5.2 m//s`.
most probable speed = speed which is had by maximum number of molecules
`C_(mp) = 4 km//s`.