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lambda=(CP)/(Cv), Find gamma(eq)required...

`lambda=(C_P)/(C_v)`, Find `gamma_(eq)`required for the mixture containing 1 mole of Gas A, 2 mole of Gas B such that `gamma` of `A= gamma_(1)` and `gamma` of `B= gamma_2` (and it is given that `C_P=C_V + R`)

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`(C_P)_("eq")=(1)/(1+2)xx(C_P)_A+(2)/(1+2)xx(C_P)_B`
`(C_v)_("eq")=(1)/(1+2)xx(C_v)_A+(2)/(1+2)xx(C_v)_B`
`((C_P)_A)/((C_v)_A)=gamma_(1)=((C_v)_A+R)/((C_v)_A)=gamma_(1)`
`implies (R)/(gamma_(1)-1)=(C_v)_A, (R gamma_(1))/(gamma_(1)-1)=(C_P)_A`
Similarly,
`(R)/(gamma_(2)-1)=(C_v)_B, (R gamma_(2))/(gamma_(2)-1)=(C_P)_B`
`gamma_("eq")=(1/3(C_P)_A+2/3(C_P)_B)/(1/3(C_v)_A+2/3(C_v)_B)`
`=((gamma_(1))/(gamma_(1)-1)+(2gamma_(2))/(gamma_(2)-1))/((1)/(gamma_(1)-1)+(2)/(gamma_(2)-1))=(3gamma_(1)gamma_2-gamma_(1)-2gamma_2)/(gamma_(1)+gamma_2-2)`
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