Speed Distribution of Ideal Gasses Video Lessons

Concept

# Problem: Suppose you could suddenly increase the speed of every molecule in a gas by a factor of 2. A. Would the rms speed of the molecules increase by a factor of 21/2, 2, or 22? Explain.B. Would the gas pressure increase by a factor of 21/2, 2, or 22? Explain.

###### FREE Expert Solution

The ratio of final rms speed to the initial rms speed is expressed as:

$\overline{)\frac{{\mathbf{v}}_{\mathbf{frms}}}{{\mathbf{v}}_{\mathbf{0}\mathbf{rms}}}{\mathbf{=}}\sqrt{\frac{\mathbf{\left[}{\mathbf{\left(}{\mathbf{v}}_{\mathbf{f}}\mathbf{\right)}}^{\mathbf{2}}{\mathbf{\right]}}_{\mathbf{avg}}}{{\mathbf{\left(}{{\mathbf{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{\right)}}_{\mathbf{avg}}}}}$

The pressure is expressed as:

$\overline{){\mathbf{P}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{3}}\frac{\mathbf{M}}{\mathbf{V}}{{{\mathbf{v}}}_{\mathbf{0}\mathbf{r}\mathbf{m}\mathbf{s}}}^{{\mathbf{2}}}}$

A.

The final rms speed is increased by a factor of 2.

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###### Problem Details

Suppose you could suddenly increase the speed of every molecule in a gas by a factor of 2.

A. Would the rms speed of the molecules increase by a factor of 21/2, 2, or 22? Explain.

B. Would the gas pressure increase by a factor of 21/2, 2, or 22? Explain.