A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P _ 0 , volume V _ 0 and temperature T _ 0 . If the gas mixture is adiabatically compressed to a

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Correct answer: A. The final pressure of the gas mixture after compression is in between 9 P _ 0 and 10 P _ 0 .

cases Here, n _ 1 = 5, & C _ P _ 1 = (5)/(2)R, & C _ V _ 1 = (3)/(2)R n _ 2 = 1, & C _ P _ 2 = (7)/(2)R, & C _ V _ 2 = (5)/(2)R cases γ _ mix = n _ 1 C _ P _ 1 + n _ 2 C _ P _ 2 n _ 1 C _ V _ 1 + n _ 2 C _ V _ 2 = (8)/(5) = 1.6 Work done, W = P _ 1 V _ 1 - P _ 2 V _ 2 γ - 1 , (Inadiabaticprocess) Now, for adiabatic compression P _ 1 V _ 1 ^ r = P _ 2 V _ 2 ^ r ⇒ P _ 0 V _ 0 ^ 8 / 5 = P _ 2 ( V _ 0 4 ) ^ 8 / 5 ⇒ P _ 2 = 9.2 P _ 0 ⇒ (A) is correct. Now, W = P _ 0 V _ 0 - 9.2 P _ 0 V _ 0 4 3 / 5 = - 13R T _ 0 ⇒ (C) is correct ∴ |W| = 13R T _ 0 Again T _ 1 V _ 1 ^ γ - 1 = T _ 2 V _ 2 ^ γ - 1 T _ 2 = T _ 1 (2) ^ 6 / 5 = 2.3 T _ 0 Average kinetic energy of gas mixture = n C _ V _ mix T _ 2 = 23R T _ 0 ⇒ (B) is incorrect

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