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1. The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is a. 1.086 : 1 b. 1 : 1.086 c. 2 : 1.086 d. 1.086 : 2

1. The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is
a. 1.086 : 1
b. 1 : 1.086
c. 2 : 1.086
d. 1.086 : 2

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
Sol. The two types of speeds are defined as; Root mean square speed (urms) = √(3RT/M) Average speed (uavg) = √(8RT/πM) For the same gas, at a given temperature, M and T are same, therefore u_rms/u_avg = √(3RT/M) ∶ √(8RT/πM) = √3 ∶ √(8/π )= √3 ∶ √2.54=1.085∶1
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

The two types of speeds are defined as;
Root mean square speed (urms) = √(3RT/M)
Average speed (uavg) = √(8RT/πM)
For the same gas, at a given temperature, M and T are same,
therefore
u_rms/u_avg = √(3RT/M) ∶ √(8RT/πM)
= √3 ∶ √(8/π )
= √3 ∶ √2.54
= 1.085∶1

Thanks and Regards

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