# At what temperature will the root-mean-square velocity of nitrogen molecules be equal

September 14, 2021 | education

| **At what temperature will the root-mean-square velocity of nitrogen molecules be equal to the first cosmic velocity (V1 = 7900m / s)?**

Given: V (mean square velocity of the taken nitrogen molecules) = 7900 m / s.

Constants: M (molar mass of nitrogen) = 0.028 kg / mol; R (universal gas constant) = 8.31 J / (mol * K).

To calculate the required temperature of taken nitrogen, use the formula: V = √ (3 * R * T / M); V ^ 2 = (3 * R * T / M) and T = V ^ 2 * M / (3 * R).

Let’s perform the calculation: T = 7900 ^ 2 * 0.028 / (3 * 8.31) ≈ 70095 K.

Answer: Nitrogen molecules can reach a speed of 7900 m / s only at a temperature of 70,095 K.

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