The molecules of a given mass of gas have an r.m.s. speed of 100 m s⁻¹ at 27°C and pressure 1.0 × 10⁵ N m⁻². When the temperature is 327°C and pressure is 0.5 × 10⁵ N m⁻², the r.m.s. speed in m s⁻¹ will be ______.
Physics · Mixed Chapter
JEE Main Practice

Question

The molecules of a given mass of gas have an r.m.s. speed of 100 m s⁻¹ at 27°C and pressure 1.0 × 10⁵ N m⁻². When the temperature is 327°C and pressure is 0.5 × 10⁵ N m⁻², the r.m.s. speed in m s⁻¹ will be ______.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Convert to kelvin: T₁ = 27 + 273 = 300 K; T₂ = 327 + 273 = 600 K. Step 2: For the same gas, vᵣₘₛ = √(3RT/M); therefore v₂/v₁ = √(T₂/T₁). Step 3: v₂ = 100 × √(600/300) = 100√2 ≈ 141.421 m s⁻¹. Step 4: Pressure does not independently affect vᵣₘₛ when gas composition and temperature are specified. Final answer: 141.4 m s⁻¹.