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Question
During an adiabatic process, the pressure of a mixture of monatomic and diatomic gases is found to be proportional to the cube of the temperature. Find the value of γ = `("C"_"P"/"C"_"V")`
Solution
In an adiabatic process, `"T"^γ"P"^(1 - γ)` = constant
`"P" ∝ "T"^3`
PT−3 = constant .........(1)
`"PT"^(γ/(1 - γ))` = constant ......(2)
`"PT"^(γ/(1 - γ)) = "PT"^-3`
Comparing the powers, `γ/(1 - γ)` = − 3 = − 3 + 3γ
2γ = 3
γ = `3/2`
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