The temperature of an ideal gas is increased from 100 K to 400 K . If 'x' is the root mean square velocity of its molecules at 100 K , r.m.s. velocity becomes

Step-by-step solution

The root mean square velocity of gas molecules follows v_ rms = 3RT M , establishing the proportionality v_ rms T . For temperatures T₁ = 100 K and T₂ = 400 K , the velocity ratio becomes v₂ v₁ = T₂ T₁ = 400 100 = 2 . Given v₁ = x , the RMS velocity at 400 K is therefore v₂ = 2x .