Question

Two gases exert pressure in the ratio 3:2 and their densities are in the ratio 2:3. then the ratio of their ems velocities is 1)2:32)3:23)2:14)1:2​

Answer 1

Answer:

vrms = √3P/pho

Vrms1/Vrms 2 = √P1×pho2/P2 × pho1

= 3/2

Answer 2

The ratio of ems velocity is 3 : 2 .

Given :

Ratio of density of gas , $\dfrac{\rho_1}{\rho_2}=\dfrac{3}{2}$

Ratio of pressure exerted by gases , $\dfrac{P_1}{P_2}=\dfrac{2}{3}$

We know, relation between pressure exerted , density and ems velocity is given by :

$P=\dfrac{\rho c^2}{3}$

For gas 1 and 2.

$P_1=\dfrac{\rho_1 c_1^2}{3}$ , $P_2=\dfrac{\rho_2 c_2^2}{3}$

Dividing $P_1\ by\ P_2$.

We get ,

$\dfrac{P_1}{P_2}=\dfrac{\dfrac{\rho_1 c_1^2}{3}}{\dfrac{\rho_2 c_2^2}{3}}\\\\\dfrac{3}{2}=\dfrac{2}{3}(\dfrac{c_1}{c_2})^2\\\\\dfrac{c_1}{c_2}=\dfrac{3}{2}$

Therefore , the ratio of $\dfrac{c_1}{c_2}=\dfrac{3}{2}$ .

Hence, this is the required solution.

Learn More :

Thermodynamics

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