For one mole of an ideal gas, increasing the temperature from `10^(@)C` to `20^(@)C`

Options

A. A) increases the average kinetic energy by two times.
B. B) increases the rms velocity by `sqrt(2)` times
C. C) increases the rms velocity by two times
D. D) increases both the average kinetic energy and rms velocity, but not significantly.

Answer

A

Explanation

Initial temperature `=283K`
Final temperature `=293K`
`KE_(1)=(3RT_(1))/(2),KE_(2)=(3RT_(2))/(2)`
`(KE_(1))/(KE_(2))=(T_(1))/(T_(2))=(283)/(293)=0.96`
`KE_(2)=1.04KE_(1)`
`v_(rms)=sqrt((3RT)/(M))`
`(v_(1))/(v_(2))=sqrt((T_(1))/(T_(2)))rArrsqrt((283)/(293))`
`v_(2)=v_(1)sqrt((293)/(283))=1.02v_(1)`
Both average K.E. and rms velocity increase but not significantly.