One gram mole of an ideal gas A with the ratio of constant pressure and constant volume specific heats γ A = 5 / 3 is mixed with n gram moles of another ideal gas B with γ B = 7 / 5 . If the γ for the mixture is 19 / 13 , then what will be the value of n ?

Step-by-step solution

By using formula, γ mixture = μ 1 C p 1 + μ 2 C p 2 μ 1 + μ 2 μ 1 C u 1 + μ 2 C v 2 μ 1 + μ 2 γ mixture = μ 1 C p 1 + μ 2 C p 2 μ 1 C v 1 + μ 2 C v 2 = μ 1 γ 1 γ 1 - 1 R + μ 2 γ 2 γ 2 - 1 R μ 1 R γ 1 - 1 + μ 2 R γ 2 - 1 or γ mixture = μ 1 γ 1 γ 2 - 1 + μ 2 γ 2 γ 1 - 1 μ 1 γ 2 - 1 + μ 2 γ 1 - 1 It is given, γ mixture = 19 13 γ 1 = 5 3