Question

what is the ratio of RMS velocities (U1/U2 ) for a gas when at constant pressure T is douled​

Answer 1

Answer:

Kinetic gas equation, for one mole gas is PV = 1/3 Mu^2 where, P = pressure of gasV = Volume of gasM = Molecular mass of gasu = root mean square velocity

Answer 2

To find:

The ratio of RMS velocities (U1/U2 ) for a gas when at constant pressure T is doubled?

Calculation:

Let initial RMS VELOCITY be at temperature T:

$\rm \: u_{1} = \sqrt{ \dfrac{3RT}{m} }$

Now, at double temperature, new RMS VELOCITY will be :

$\rm \: u_{2} = \sqrt{ \dfrac{3R(2T)}{m} }$

Now, required ratio will be :

$\rm \dfrac{ u_{1}}{ u_{2}} = \dfrac{ \sqrt{ \frac{3RT}{m} } }{ \sqrt{ \frac{3R(2T)}{m} } }$

$\rm \implies\dfrac{ u_{1}}{ u_{2}} = \dfrac{1}{ \sqrt{2} }$

So, required ratio is 1 : √2.