Question

Two containers A & B contain ideal gases helium and oxygen respectively. Volume of both containers are equal and pressure is also equal. Container A has twice the number of molecules than container B then if v_A&v_B represent the rms speed of gases in containers A & B respectively, then -

A

• A. $\frac{v_{A}}{v_{B}}$ = $\sqrt{2}$
• B. $\frac{v_{A}}{v_{B}}$= 4
• C. $\frac{v_{A}}{v_{B}}$ = 2
• D. $\frac{v_{A}}{v_{B}}$ = $\sqrt{8}$

Answer 1

Answer: (C)

$\frac{v_{A}}{v_{B}}$ = 2

Answer 2

T_A = $\frac{P_{A}V_{A}}{n_{A}R}$ and T_B = $\frac{P_{B}V_{B}}{n_{B}R}$

Given, P_A = P_B , V_A = V_B and n_A = 2n_B

\ T_A = $\frac{T_{B}}{2}$

Now, $\frac{V_{A}}{V_{B}} = \sqrt{\frac{T_{A}}{T_{B}} \times \frac{M_{B}}{M_{A}}}$ = 2