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