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(II) Show that for a mixture of two gases at the same temperature, the ratio of their rms speeds is equal to the inverse ratio of the square roots of their molecular masses.

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$\frac{\left(v_{r m s}\right)_{2}}{\left(v_{r m s}\right)_{1}}=\sqrt{\frac{m_{1}}{m_{2}}}$

Physics 101 Mechanics

Chapter 18

Kinetic Theory of Gases

Temperature and Heat

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October 15, 2020

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(II) Show that for a mixtu…

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Show that for a mixture of…

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Show that, in two gases at…

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(II) Show that the rms spe…

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Okay, so we're doing Chapter 18 Problem 11. So says chauffeur, a mixture of two gases, same temperature, so same teeth. Um, the ratio of their arm, SPD's equal to the inverse ratio of the square roots of their molecular masses. Okay, so we want to find the ratio of the our messes the r m s of one molecule over the first or one mixture of one one conglomerate of gas. Over the 2nd 1 There's two different gases. So this is for guests to you and gas one night. So the ratio of each gases arm s speed, so we know the army's speed is given us three K b t over. Mm. Now, we already said they were at the same temperature in three, and bull's been constant on the same. So the only difference here, other masses. And now we can just cancel that out. So this now becomes scrape of and one over into, or this is square into over and one in first, which is exactly what we wanted to show. Right. So says show that the mixture of two gases, same temperature, the ratio of the armistice, this is equal to the inverse yes ratio? Yes, of their square roots of my career masses. So yep, we got it all. That's

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