Новое решение
en/5.3.9.md
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| + | ### Statement | ||
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| + | $5.3.9.$ [Insert the problem statement] | ||
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| + | ### Solution | ||
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| + | We'll consider molecules $A$ as impurities, meaning that the number of collisions of molecules $A$ with each other is much less than the number of collisions with molecules of gases $B_{1}$ and $B_{2}$. We'll also assume that the temperature is the same in all cases. This means we can assume that: | ||
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| + | $$\frac{D_{1}}{D_{2}}=\frac{(R_{A} + R_{B_{2}})^{2}}{(R_{A} + R_{B_{1}})^{2}}$$ | ||
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| + | Number of collisions in the mixture: | ||
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| + | $$\nu_{12}=\pi\cdot (R_{A} + R_{B_{1}})^{2}\cdot n_{1}\cdot <\upsilon_{sq_{A}}> + \pi\cdot (R_{A} + R_{B_{2}})^{2}\cdot n_{2}\cdot <\upsilon_{sq_{A}}>$$ | ||
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| + | Let's write down the ratio of $D_{1}$ to $D_{12}$, after some transformations we get: | ||
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| + | $$\frac{D_{1}}{D_{12}}=\frac{(R_{A} + R_{B_{1}})^{2}\cdot n_{1} + (R_{A} + R_{B_{2}})^{2}\cdot n_{2}}{(R_{A} + R_{B_{1}})^{2}\cdot n}$$ | ||
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| + | Let's use the relation for $D_{1}$ and $D_{2}$: | ||
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| + | $$\frac{D_{1}}{D_{12}}=\frac{n_{1} + \frac{D_{1}}{D_{2}}\cdot n_{2}}{n}$$ | ||
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| + | Expressing $D_{12}$ we get: | ||
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| + | $$D_{12}=\frac{n\cdot D_{1}\cdot D_{2}}{n_{1}\cdot D_{2} + n_{2}\cdot D_{1}}$$ | ||
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| + | #### Answer | ||
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| + | [Insert a concise answer or boxed result] | ||
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| ### Statement | |||
| $5.3.9.$ [Insert the problem statement] | |||
| ### Solution | |||
| We'll consider molecules $A$ as impurities, meaning that the number of collisions of molecules $A$ with each other is much less than the number of collisions with molecules of gases $B_{1}$ and $B_{2}$. We'll also assume that the temperature is the same in all cases. This means we can assume that: | |||
| $$\frac{D_{1}}{D_{2}}=\frac{(R_{A} + R_{B_{2}})^{2}}{(R_{A} + R_{B_{1}})^{2}}$$ | |||
| Number of collisions in the mixture: | |||
| $$\nu_{12}=\pi\cdot (R_{A} + R_{B_{1}})^{2}\cdot n_{1}\cdot <\upsilon_{sq_{A}}> + \pi\cdot (R_{A} + R_{B_{2}})^{2}\cdot n_{2}\cdot <\upsilon_{sq_{A}}>$$ | |||
| Let's write down the ratio of $D_{1}$ to $D_{12}$, after some transformations we get: | |||
| $$\frac{D_{1}}{D_{12}}=\frac{(R_{A} + R_{B_{1}})^{2}\cdot n_{1} + (R_{A} + R_{B_{2}})^{2}\cdot n_{2}}{(R_{A} + R_{B_{1}})^{2}\cdot n}$$ | |||
| Let's use the relation for $D_{1}$ and $D_{2}$: | |||
| $$\frac{D_{1}}{D_{12}}=\frac{n_{1} + \frac{D_{1}}{D_{2}}\cdot n_{2}}{n}$$ | |||
| Expressing $D_{12}$ we get: | |||
| $$D_{12}=\frac{n\cdot D_{1}\cdot D_{2}}{n_{1}\cdot D_{2} + n_{2}\cdot D_{1}}$$ | |||
| #### Answer | |||
| [Insert a concise answer or boxed result] | |||