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Question
A mixture contains 1 mole of helium (Cp = 2.5 R, Cv = 1.5 R) and 1 mole of hydrogen (Cp= 3.5 R, Cv = 2.5 R). Calculate the values of Cp, Cv and γ for the mixture.
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Solution
Specific heat at constant pressure of helium, Cp' = 2.5 R
Specific heat at constant pressure of hydrogen, Cp" = 3.5 R
Specific heat at constant volume of helium, Cv' = 1.5 R
Specific heat at constant volume of hydrogen, Cv" = 2.5 R
n1 = n2 = 1 mol
dU = nCvdT
For the mixture of two gases,
dU1 +dU2 = 1 mol
[n1 + n2] CvdT = n1C'vdT + n2C"vdT,
where Cv is the heat capacity of the mixture
`=> "C"_"v" =("n"_1"C"'_"v" + "n"_2"C"''_"v")/("n"_1+"n"_2)`
`= (1.5"R" +2.5"R")/2 =2"R"`
Cp = Cv + R = 2R + R = 3R
`gamma = "C"_"p"/"C"_"v" = (3"R")/(2"R") = 1.5`
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