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Question

One mole of ideal monoatomic gas (γ=53) is mixed with one mole of diatomic gas (γ=75). What is γ for the mixture? γ denotes the ratio of specific heat at constant pressure, to that at constant volume.


A

32

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B

2315

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C

3523

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D

43

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Solution

The correct option is A

32


For a monoatomic gas, Cv=3R2 and for a diatomic gas, Cv=5R2. Since one mole of each gas is mixed together, the Cv of the mixture will
Cv=12[3R2+5R2]=2R
Now CpCv=R. Therefore, for the mixture, Cp=R+Cv=R+2R=3R. Hence, the ratio of the specific heats of the mixture is
γ=CpCv=3R2R=32,


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