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Relating Translational KE and T

7g of N 2 i...

Question

7g of $N_{2}$ is present at $127$ and 16g of $O_{2}$ present at $127$ calculate the ratio of K.E, calculate the ratio of ${K . E}_{A v g}$ of $N_{2}$ and $O_{2}$ .

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Solution

Average $K E = \frac{3}{2} K_{B} T$ where $K_{B}$ = Boltzmann constant
Hence $(K E)_{a v g}$ depends only on temperature. Since both the gases are at sme temperature, the ratio of $K . E_{a v g}$ of $N_{2}$ & $O_{2}$ is $1 : 1$ .

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