One mole of an ideal monoatomic gas (y=5/3)is mixed with one mole of a diatomic gas(y=7/5). (Y denotes the ratio of specific heat at constant pressure, to that at constant volume ) find y for the mixture?

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Solution

Dear Student

y = C_p/ C_v

For monoatomic gas

C_v = R / y - 1 = 3R/2

For Diatomic gas
C_v = 5R/2

Formula for Heat capacity of mixture (C_v)_mixture = ( n₁C_v1 + n₂C_v2 ) / (n₁ + n₂)
= (1x 3R/2 + 1x 5R/2 ) / (1+1)
= 2 R
by Meyer 's relation

(C_p)_mixture - (C_v)_mixture = R
(C_p)_mixture = 2R + R = 3R

ϒ_mixture = (C_p)_mixture/ (C_v)_mixture
= 3R / 2R = 1.5

thanks
regards

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