The root mean square (rms) velocity ($v_{rms}$) of ideal gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass . The pressure ($P$) does not explicitly affect $v_{rms}$ if the temperature is known, as $v_{rms}$ depends solely on $T$ for a given gas.

Given:

1. Initial state: $v_1 = 200 \text{ m s}^{-1}$, $T_1 = 27^{\circ}\text{C} = 300 \text{ K}$.
2. Final state: $T_2 = 127^{\circ}\text{C} = 400 \text{ K}$.

Calculation: Using the proportionality $v_{rms} \propto \sqrt{T}$: $\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$ $\frac{v_2}{200} = \sqrt{\frac{400}{300}} = \sqrt{\frac{4}{3}} = \frac{2}{\sqrt{3}}$ $v_2 = 200 \times \frac{2}{\sqrt{3}} = \frac{400}{\sqrt{3}} \text{ m s}^{-1}$.