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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.

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2 Answers 2

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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?

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$\sqrt{2}$ ? 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

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.

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

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