One litre glass bulb contains `2 xx10^(21)` molecules of nitrogen at a pessure of `7.57 xx 10^(3)` Newton `m^(-2)`. Find the RMS velocity and temperature of the gas. If the ratio of most probable velocity and RMS velocity is 0.82, find the most probable velocity of nitrogen gas at the same temperature.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Convert Pressure to Atmospheres
The pressure given is \( P = 7.57 \times 10^3 \, \text{N/m}^2 \). We need to convert this to atmospheres using the conversion factor \( 1 \, \text{atm} = 1.013 \times 10^5 \, \text{N/m}^2 \).

\[ P_{\text{atm}} = \frac{7.57 \times 10^3}{1.013 \times 10^5} \approx 0.0747 \, \text{atm} \]
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