Chapter 6, Problem 77E

Interpretation Introduction

Interpretation:

The temperature at which ${\text{u}}_{\text{rms}}$ of neon gas is equal ${\text{u}}_{\text{rms}}$ of helium gas at 300 K should be calculated.

Concept introduction:

${\text{u}}_{\text{rms}}$ of any gas molecule can be defined as the root mean square velocity of gaseous molecules.

The mathematical representation of ${\text{u}}_{\text{rms}}$ is:

${\text{u}}_{\text{rms}}\text{= }\sqrt{\frac{\text{3RT }}{\text{M}}}$

Here:

• R = gas constant = $\text{8}\text{.3145 J/K}\cdot \text{mole}$
• T = Temperature in K
• M = Molar mass ( kg/mole)

${\text{u}}_{\text{rms}}$, molar mass and T are related with given relation:

$\frac{{\text{u}}_{{\text{rms}}_{\text{1}}}}{{\text{u}}_{{\text{rms}}_{\text{2}}}}\text{= }\sqrt{\frac{{\text{M}}_{\text{2}}\times {\text{ T}}_{\text{1}}}{{\text{M}}_{\text{1}}\times {\text{ T}}_{\text{2}}}}$