Two moles of an ideal gas, with C P C V = 5 3 , are mixed with three moles of another ideal gas C P C V = 4 3 . The value of C P C V for the mixture is

Step-by-step solution

Let n₁,n₂ be the number of moles of gases 1 and 2 . We have C_ p₁ C_ v₁ = 5 3 and We know C_ p₁ =C_ v₁ +R 5C_ v₁ 3 =C_ v₁ +R, 2C_ v₁ 3 R₁,C_ v₁ = 3R 2 A and C_ p₁ =C_ v_ 1 +R= 5R 2 Also, C_ p_ 2 C_ v_ 2 = 4 3 and C_ p₂ =C_ v₂ +R 4C_ v_ 2 3 =C_ v_ 2 +R, C_ v_ 2 3 =R,C_ v_ 2 =3R C_ p_ 2 =C_ v_ 2 + R=4R Now C_ v_ mix = n₁C_ v_ 1 +n₂C_ v_ 2 n₁+n₂ = 2 3R 2 +3 3R 2+3 = 3R+9R 5 = 12R 5 C_ p_ mix = n₁C_ p_ 1 +n₂C_ p_ 2 n₁+n₂ = 2 5R 2 +3 4R 2+3 = 17R 5 l_ mix = C_ p_ mix C_ v_ mix = 17 12 =1.4166=1.42 .