At what temperature, average velocity of oxygen molecule is equal to the rms velocity at `27^(@)C` ?

Explanation

To find the temperature at which the average velocity of an oxygen molecule is equal to the root mean square (RMS) velocity at 27°C, we can follow these steps:

### Step 1: Understand the formulas
The average velocity (\(v_{avg}\)) and the root mean square velocity (\(v_{rms}\)) of gas molecules can be expressed in terms of temperature.

The formula for the RMS velocity is given by:
\[
v_{rms} = \sqrt{\frac{3kT}{m}}
...