1.

N(lt100) molecule of a gas have velocities 1,2,3….N, km/s respectively. Then

Answer»

rms SPEED and average speed of molecules are same
ratio of rms speed to average speed is `sqrt(((2N+1)(N+1))/(6N))`
ratio of rms speed to average speed is `sqrt(((2N+1)(N+1))/(6))`
ratio of rms speed to average speed of a MOLECULE `(2)/(sqrt(6))sqrt(((2N+1))/((N+1)))`

SOLUTION :Average speed,
`v_(av)=(1+2+...+N)/(N)=(N(N+1))/(2N)=(N+1)/(2)`
rms speed,
`v_(rms)=sqrt((1^(2)+2^(2)+3^(2)+...+N^(2))/(N))`
`=sqrt((N(N+1)(2N+1))/(6N))=sqrt(((N+1)(2N+1))/(6))`
`(v_(rms))/(v_(av))=sqrt(((N+1)(2N+1))/(6))xx(2)/((N+1))=(2)/(sqrt(6))=sqrt(((2N+1)/(N+1)))`


Discussion

No Comment Found

Related InterviewSolutions