The ratio between the root mean square speed of H2 at 50 K and that of O2 at 800 K is

Question

The ratio between the root mean square speed of H2 at 50 K and that of O2 at 800 K is (A) 4 (B) 2 (C) 1 (D) (1/4)

Tardigrade Admin · Accepted Answer

Expression of rms is, u rms =√(3 R T/M) ⇒ (u rms ( H 2 text at 50 K )/u rms ( O 2 text at 800 K ))=(√(3 R × 50/2)/√(3 R × 800)32) =√(50/2) × (32/800)=1

Q. The ratio between the root mean square speed of $H_{2}$ at $50 K$ and that of $O_{2}$ at $800 K$ is

4

2

1

$\frac{1}{4}$

Expression of rms is, $u_{r m s} = \frac{3 RT}{M}$
$\Rightarrow \frac{u _{r m s} ( H _{2} at 50 K )}{u _{r m s} ( O _{2} at 800 K )} = \frac{\frac{3 R \times 50}{2}}{\frac{3 R \times 800}{32}}$
$= \frac{50}{2} \times \frac{32}{800} = 1$

Q. The ratio between the root mean square speed of H2​ at 50K and that of O2​ at 800K is

4

2

1

41​

Expression of rms is, urms​=M3RT​​ ⇒urms​(O2​ at 800K)urms​(H2​ at 50K)​=323R×800​​23R×50​​​ =250​×80032​​=1

Q. The ratio between the root mean square speed of $H_{2}$ at $50 K$ and that of $O_{2}$ at $800 K$ is

$\frac{1}{4}$

Expression of rms is, $u_{r m s} = \frac{3 RT}{M}$
$\Rightarrow \frac{u _{r m s} ( H _{2} at 50 K )}{u _{r m s} ( O _{2} at 800 K )} = \frac{\frac{3 R \times 50}{2}}{\frac{3 R \times 800}{32}}$
$= \frac{50}{2} \times \frac{32}{800} = 1$