Find average molecular speed in gas when temperature doubles?

Question

I have the following formula.
enter image description here The task just says what happens to average speed of the molecules in a gas when the absolute temperature doubles? I don't know how to go about tasks like this. What am I to solve for to hopefully find something like this: T = factor * speed. I'm not comfortable just multiplying with two on the left side.

score 3 · Accepted Answer · answered Oct 16 '12 at 14:19

3

I would begin by isolating $v$. We have $$\frac{3Tk}{m} = v^2 \implies v = \sqrt{\frac{3Tk}{m}}$$ so for a given $T$, we know how to find $v$. What happens if we substitute $2T$ for $T$? What extra factor do we gain?

answered Oct 16 '12 at 14:19

EuYu

41,421

1

$\sqrt{2}$ ? I think.. – Algific Oct 16 '12 at 14:29
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Yes, that's it. Every time your temperature doubles, your speed increases by a factor of $\sqrt{2}$. – EuYu Oct 16 '12 at 14:30

score 2 · Answer 2 · answered Oct 16 '12 at 14:19

2

You can multiply by $2$ on both sides. $\frac 32 \times 2=3,\ \frac 12 \times 2=1$ then you want to isolate $v$ as that is the output you are being asked for, not $T$ which is the input.

answered Oct 16 '12 at 14:19

Ross Millikan

374,822

I found the comment on input and output useful so thanks. – Algific Oct 16 '12 at 14:58

Find average molecular speed in gas when temperature doubles?

2 Answers2