When temperature of an ideal gas is increased from 27⁰C to 227⁰C,

When Temperature Of An Ideal Gas Is Increased From 27c Physics QuestionWhen Temperature Of An Ideal Gas Is Increased From 27c Physics Question

When temperature of an ideal gas is increased from 27⁰C to 227⁰C, its r.m.s. speed changes from 400 m/s to Vs. The Vs is

Options

(a) 516 m/s
(b) 450 m/s
(c) 310 m/s
(d) 746 m/s

Correct Answer:

516 m/s

Explanation:

[ʋ(rms)]² ∝ absolute temperature
[ʋ₂ / ʋ₁]² = T₂ / T₁ ⇒ (ʋ₂ / 400) = √[(273+227) / (273+27)] = √(500 / 300) = √(5 / 3)
.·. ʋ₂ = 400 × √(5 / 3) = 400 × √1.67 = 516 m/s

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