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Two containers are at the same temperature. The gas in the first container is at pressure $p_{1}$ and has molecules with mass $m_{1}$and root-mean-square speed $v_{\text { rmst }}$ . The gas in the second is at pressure 2$p_{1}$ and has molecules with mass $m_{2}$ and average speed $v_{\mathrm{avg} 2}=2 v_{\mathrm{msl}} \cdot$ Find the ratio $m_{1} / m_{2}$ of the masses of their molecules.

4.71

Physics 101 Mechanics

Chapter 19

The Kinetic Theory of Gases

Temperature and Heat

Cornell University

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Winnipeg

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Now we're given the pressures molecular masses on the Artemus and the average off particles two sets of gases You know that we oughta mus is squared off three rd by m So we are to miss one. It's quid off three our teeth by m one. Similarly, we average too. We know the formula is squared off Aid Artie by pie. Um, so that's a tarty Bye. Hi M to Now we know that the average two is twice we are miss one. So that's two times It's weird off three. Artie by m one. We also know that Muller mask is molecular mass times I've got your number. So em one by m too is someone by MT So from this equation, by swearing on both sides on canceling Artie, they see that 64 by hi M toe is equal new four times three by m one, now 64 4 times 16 in 64. Which means And when I am too, is which is also equal toe small in one very small himto is equal. Do three by by 16. And that is a uh what? I'm sorry. This is square just eight. Artie. So This is not 64. This is just eight I. So when you cancel it before, it turns out to be just too, which means this is simply three bye bye, too. On three. Pervy, too, is simply 4.71 so the ratio's off. Molecular masses is 4.71 simple as that.

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