Question

The rms speed of a gas molecule is 300m/s. Calculate the rms speed if the molecular weight is doubled while the temperature is halved.

Answer 1

Answer:

gets reduced by half of the velocity rms

Answer 2

The new speed becomes half of the initial speed.

Explanation:

The RMS speed of a gas molecule is given by :

$v=\sqrt{\dfrac{3RT}{M}}$

R is the gas constant

T is temperature

M is the molecular weight of the gas molecule

According to given condition, if the molecular weight is doubled while the temperature is halved such that,

M' = 2M

and

T' = (1/2) T

New speed becomes,

$v'=\sqrt{\dfrac{3RT'}{M'}}$

$v'=\sqrt{\dfrac{3R(T/2)}{2M}}$

$v'=\dfrac{1}{2}\times \sqrt{\dfrac{3RT}{M}}$

So, the new speed becomes half of the initial speed. Hence, this is the required solution.

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