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

At What Temperature Will The Rms Speed Of Air Molecules Physics QuestionAt What Temperature Will The Rms Speed Of Air Molecules Physics Question

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

Options

(a) 519⁰C
(b) 619⁰C
(c) 719⁰C
(d) 819⁰C

Correct Answer:

819⁰C

Explanation:

v(rms) = √(3RT / M)
At T = T₀, v(rms) = √(3RT / M)
But at temperature T, v(rms) = 2 × √(3RT₀ / M)
⇒ √(3RT / M) = 2 √(3RT₀ / M) ⇒ √T = √(4T₀) ⇒ T = 4T₀
T = 4 × 273 K = 1092 K
Therefore, T = 819°C

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