Question

The molecules of a given mass of a gas have an r.m.s. velocity of 200 m s⁻¹ at 27°C and 1.0 × 10⁵ N m⁻² pressure. When the temperature and pressure of the gas are 127°C and 0.05 × 10⁵ N m⁻², respectively, the r.m.s. velocity of its molecules is:

• A. \(100\sqrt{2}\)
• B. \(\frac{400}{\sqrt{3}}\)
• C. \(\frac{100\sqrt{2}}{3}\)
• D. (100)/(3)

Hint:

RMS speed is independent of pressure; it depends only on absolute temperature.

Answer 1

The Correct Option is A

Step 1: RMS velocity depends only on temperature: vᵣms ∝ √(T)
Step 2: Convert temperatures to Kelvin: T₁ = 300K, T₂ = 400K
Step 3: v₂ = 200 √((400)/(300)) = 200√((4)/(3)) = 100√(2)