Question

find rms and most probable speed of CO2 gas at 27°c.​

Answer 1

$\huge{\textbf{\underline{RMS Vs MPS}}}$

Q. Find RMS and MPS of $CO_2$ gas at 27°C.

$\huge{\textbf{\underline{Solution:-}}}$

Temperature = 27°C

Change it in to Kelvin = 273 + 27

= 300 K.

Molecular mass = 44

$\large{\textbf{\underline{RMS speed of gas is :-}}}$

$\boxed{RMS =\sqrt{\dfrac{3RT}{M}}}$

$RMS = \sqrt{\dfrac{3 \times 8.32 \times 300}{44}}$

$RMS = \sqrt{\dfrac{7488}{44}}$

$RMS = \sqrt{170.18}$

$\therefore RMS_{CO_{2}} = 13. 04 m/s$

$\large{\textbf{\underline{MPS speed of gas is :-}}}$

$\boxed{MPS = \sqrt{\dfrac{2RT}{M}}}$

$MPS = \sqrt{\dfrac{2\times 8.32 \times 300}{44}}$

$MPS = \sqrt{\dfrac{4992}{44}}$

$MPS = \sqrt{113.45}$

$\therefore MPS_{CO_{2}} = 10 .65 m/s$