If the r.m.s speed of a gas molecule at 27°C is 100$\sqrt{2}$ ms^-1, the r.m.s speed at 327°C would be

Root Mean Square (r.m.s) Speed Calculation

The root mean square (r.m.s) speed of gas molecules is given by the relation:

v_rms ∝ √T

Where T is the absolute temperature (in Kelvin). Let’s compare the two temperatures:

• Initial temperature: 27°C = 27 + 273 = 300 K
• Final temperature: 327°C = 327 + 273 = 600 K

The ratio of the r.m.s speeds is:

v_{rms, final} / v_{rms, initial} = √(T_final / T_initial)

Substitute the given values:

v_{rms, final} / 1002 = √(600 / 300) = √2

Therefore:

v_{rms, final} = 1002 × √2 ≈ 1416 ms^-1

None of the provided options match exactly, but the calculation shows that the final r.m.s speed would be approximately 1416 ms^-1, not any of the listed choices (100, 200, 300, 400).