A gaseous mixture enclosed in a vessel consists of one mole of a gas A with γ = 3 5 and some amount of gas B with γ = 5 7 at a temperature T . The gases A and B do not react with each other and ar

Question

A gaseous mixture enclosed in a vessel consists of one mole of a gas A with γ = 3 5 ​ and some amount of gas B with γ = 5 7 ​ at a temperature T . The gases A and B do not react with each other and are assumed to be ideal. Find the number of moles of the gas B if γ for the gaseous mixture is 13 19 ​ .

TestHub · Accepted Answer

C v ​ = γ − 1 R ​ gas A: = 2 3 ​ R C p ​ = 2 5 ​ R Gas B: = 2 5 ​ R C p ​ = 2 7 ​ R Mixture ( 1 mol A + n mol B): γ = 2 3 ​ + 2 5 ​ n 2 5 ​ + 2 7 ​ n ​ = 13 19 ​ 13 ( 2.5 + 3.5 n ) = 19 ( 1.5 + 2.5 n ) ⇒ 32.5 + 45.5 n = 28.5 + 47.5 n 2 n = 4 ⇒ n = 2 Answer: 2.

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