Question

..
At a given temperature the ratio of RMS and Average velocities is
a) 1.086:1
b) 1:1.086
c) 2:1.086
d) 1.086:2
​

Answer 1

Explanation:

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

Step by step explanation:

At particular temperature, velocity of gas molecule can be calculated by the following formula.

Root mean square speed --- \bold{v_{rms}=\sqrt{\frac{3RT}{M}}}v

rms

=

M

3RT

.............(1)

Average sped of gas ----- \bold{v_{average}=\sqrt{\frac{8RT}{M}}}v

average

=

M

8RT

..............(2)

Let's take a ratio of equation(1) and (2)

\

\Rightarrow 1.086:1⇒1.086:1

Therefore, The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is 1.086 : 1 .

Hence,

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Answer 2

Answer:

$\huge\color{violet}\mathfrak{Hey\:Mate\:Your\:Answer}$

Explanation:

The expression for the root mean square velocity is$(u _{rms}) = \sqrt \frac{3RT}{M}$

The expression for the average speed is

$(u_{avg}) = \sqrt \frac{8RT}{πM}$

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:

$\frac{u_{rms} }{u_{avg} } = \sqrt \frac{3RT}{M} : \sqrt \frac{8RT}{\pi \: M} = \sqrt{3} : \sqrt \frac{8}{\pi} = \sqrt{3} : \sqrt{2.54} = 1.181:1$

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