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A mixture is prepared by combining 1 mole of a monatomic gas with 2 moles of a diatomic gas. During a certain process, the molar heat capacity of the mixture is measured to be 3R. The polytropic index for this process is:

1. −1/5
2. 1/5
3. 2/5
4. −2/5

Correct answer: −1/5

Solution

Mixture Cv = (1*1.5R + 2*2.5R)/3 = 13R/6. With C = Cv + R/(1-n) = 3R: R/(1-n) = 3R - 13R/6 = 5R/6, so 1-n = 6/5 and n = -1/5.

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