At what temperature will the rms speed of air molecules be double that NTP?

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At what temperature will the rms speed of air molecules be double that NTP?

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verified

The correct answer is 1092K or 819°C

Explanation ::

We have $$V_{rms}={\sqrt{3RT\over M}}$$  --at T=$$T_0 (NTP)$$

$$V_{rms}={\sqrt{3RT_0\over M}}$$

But at temperature T

$$V_{rms}={2\sqrt{3RT\over M}}$$

$$\therefore \sqrt{3RT\over M}=2{\sqrt{3RT_0\over M}}$$

$$\sqrt T = \sqrt{4T_0}$$

T= 4× 273 k

T=1092 K

Or

T=819°C

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Thanks the answer is correct varified by team Brainiak