A cubical box with porous walls containing an equal number of O2 and H2 molecules is placed in a larger evacuated chamber. The entire system is maintained at constant temperature T. The ratio of root mean square speed of O2 molecules to that of the H2 molecules is

Question

A cubical box with porous walls containing an equal number of O2 and H2 molecules is placed in a larger evacuated chamber. The entire system is maintained at constant temperature T. The ratio of root mean square speed of O2 molecules to that of the H2 molecules is (A) (1/2 √2) (B) (1/4) (C) (1/√2) (D) √2

Tardigrade Admin · Accepted Answer

∵ Vr m s=√(&gamma; R T/M) ⇒ ((Vr m s) O2/(Vr m s) H2)=√((M0) H2/(M0) O2) =√(2/32)=(1/4)

Q. A cubical box with porous walls containing an equal number of $O_{2}$ and $H_{2}$ molecules is placed in a larger evacuated chamber. The entire system is maintained at constant temperature $T .$ The ratio of root mean square speed of $O_{2}$ molecules to that of the $H_{2}$ molecules is

$\frac{1}{2 2}$

$\frac{1}{4}$

$\frac{1}{2}$

$2$

$∵$ $V_{r m s} = \frac{γ RT}{M}$
$\Rightarrow \frac{( V _{r m s} ) O _{2}}{( V _{r m s} ) H _{2}} = \frac{( M _{0} ) H _{2}}{( M _{0} ) O _{2}}$
$= \frac{2}{32} = \frac{1}{4}$

Q. A cubical box with porous walls containing an equal number of O2​ and H2​ molecules is placed in a larger evacuated chamber. The entire system is maintained at constant temperature T. The ratio of root mean square speed of O2​ molecules to that of the H2​ molecules is

22​1​

41​

2​1​

2​

∵ Vrms​=MγRT​​ ⇒(Vrms​)H2​(Vrms​)O2​​=(M0​)O2​(M0​)H2​​​ =322​​=41​

Q. A cubical box with porous walls containing an equal number of $O_{2}$ and $H_{2}$ molecules is placed in a larger evacuated chamber. The entire system is maintained at constant temperature $T .$ The ratio of root mean square speed of $O_{2}$ molecules to that of the $H_{2}$ molecules is

$\frac{1}{2 2}$

$\frac{1}{4}$

$\frac{1}{2}$

$2$

$∵$ $V_{r m s} = \frac{γ RT}{M}$
$\Rightarrow \frac{( V _{r m s} ) O _{2}}{( V _{r m s} ) H _{2}} = \frac{( M _{0} ) H _{2}}{( M _{0} ) O _{2}}$
$= \frac{2}{32} = \frac{1}{4}$