Let A and B the two gases and given : T_A M_A = 4. T_B M_B ; wher… - Vidyadip

MCQ

Let $A$ and $B$ the two gases and given : $\frac{{{T_A}}}{{{M_A}}} = 4.\frac{{{T_B}}}{{{M_B}}};$ where $T$ is the temperature and M is molecular mass. If ${C_A}$ and ${C_B}$ are the $r.m.s. $ speed, then the ratio $\frac{{{C_A}}}{{{C_B}}}$ will be equal to

✓
$2$
B
$4$
C
$1$
D
$0.5$

✓

Answer

Correct option: A.

$2$

a
$\frac{{{T_A}}}{{{M_A}}} = 4\frac{{{T_B}}}{{{M_B}}}$

$ \Rightarrow \sqrt {\frac{{{T_A}}}{{{M_A}}}} = 2\sqrt {\frac{{{T_B}}}{{{M_B}}}} $

$ \Rightarrow \sqrt {\frac{{3R{T_A}}}{{{M_A}}}} = 2\sqrt {\frac{{3RT}}{{{M_B}}}} $

$ \Rightarrow {C_A} = 2{C_B}$

$ \Rightarrow \frac{{{C_A}}}{{{C_B}}} = 2$

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