Question

1. The ratio of root mean square velocity to average velocity of
a gas molecule at a particular temperature is | (1981, 1M)
(a) 1.086:1
(b) 1: 1.086
(c) 2 : 1.086
(d) 1.086:2​

Answer 1

The ratio of root mean square velocity to average velocity of

a gas molecule at a particular temperature is (a) 1.086:1

1. Root mean square velocity is given by c= (3RT/M)^1/2

2. Average velocity is given by

v= (8RT/πM)^1/2

3. Thus the ratio c/v = (3π/8)^1/2

= 3.062/2.82

= 1.086/1

= 1.086:1

4. Thus, the correct answer is (a)

Answer 2

The ratio of root mean square velocity to average velocity is 1.181 : 1

Explanation:

The expression for the root mean square velocity is (urms ) = √ 3RT /M

The expression for the average speed is ( V avg) = √8 RT /π M

For a particular gas, at a particular temperature, M and T are constant.

Hence, the ratio of the root mean square velocity to average speed is:

(U rms) /  (U avg) = √ 3RT /M :  √8 RT /π M

(U rms) /  (U avg) =  √ 3 : √ 8 / π  

(U rms) /  (U avg) =   √ 3 :  √ 2.54

(U rms) /  (U avg) = 1.181 : 1

Thus the ratio of root mean square velocity to average velocity is 1.181 : 1

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