Air is cooled from `25^@C` to `0^@C`. Calculate the decrease in rms speed of the molecules.

Explanation

RMS speed ` u_(rms) = sqrt((3RT)/(M))`
` = sqrt(( 3 xx R xx 298 )/(M ))` ( At `25 ^@ C `)
` u_(rms) = sqrt((3RT)/(M ) ) = sqrt((3 xx R xx 273 )/( M )) ` ( At ` 0^@C `)
` (C_(rms)" at" 25^@ C )/( C_(rms) "at" 0^@ C)= sqrt(( (3R xx 298 )/(M))/((3R xx 273 )/(M )))= sqrt(( 298)/(273)) =1.045`
`1.045` units has a decreases is 0.045
for 100 parts ` to ( 100 )/( 1.045 ) xx 0.045 = 4.3 %`
` therefore ` Decrease in rms speed
`= 4.3 % ` (approxmates)