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

Step-by-step solution

The root mean square (RMS) velocity of gas molecules is defined by v_ rms = 3RT M , where R is the universal gas constant, T is the absolute temperature, and M is the molar mass. This shows that v_ rms T . For initial temperature T₁ = 100 K and initial velocity v₁ = x , and final temperature T₂ = 400 K with final velocity v₂ , the ratio becomes: v₂ x = 400 100 = 4 = 2 So v₂ = 2x , which corresponds to option C.