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

PV = nRT Ž T_A = $\frac{T_{B}}{2}$

v_rms µ$\sqrt{\frac{T}{M}}$

Ž $\frac{v_{A}}{v_{B}}$ = $\sqrt{\frac{T_{A}}{T_{B}} \times \frac{M_{B}}{M_{A}}}$ = $\sqrt{\frac{1}{2} \times \frac{16 \times 2}{4}}$

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