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An experiment you're designing needs a gas with γ= 1.63. You recall from your physics class...

An experiment you're designing needs a gas with γ= 1.63. You recall from your physics class that no individual gas has this value, but it occurs to you that you could produce a gas with γ = 1.63 by mixing together a monatomic gas and a diatomic gas. What fraction of the molecules need to be monatomic?

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Answer #1

For monatomic gas: gamma = 5/3
For diatomic gas: gamma = 7/5
Let the fraction of the monatomic molecule in the mixture to be x, the fraction of the diatomic molecule in the mixture must be 1-x. Hence:
5x/3 + (7/5)(1-x) = 1.63
5x/3-7x/5=1.63-7/5
x = (1.63-7/5)/(5/3-7/5) = 86.25%

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