A gaseous mixture consists of 16 ~g of helium and 16 ~g of oxygen. The ratio C_ p / C_ V of the mixture is

Step-by-step solution

Mass of helium, m₁=16 ~g Mass of oxygen, m₂=16 ~g Number of moles of He gas, n₁= m₁ 4 = 16 4 =4 Number of moles of O ₂ gas , n₂= m₂ 32 = 16 32 = 1 2 We know that for the mixture, aligned C_ V &= n₁ C_ V +n₂ C_ V₂ n₁+n₂ , where C_ V = f R 2 and C_ p &= n₁ C_ p₁ +n₂ C_ p₂ n₁+n₂ , where C_ p = ( f 2 +1 ) R aligned For He gas, f=3, n₁=4 For O ₂ gas, f=5, n₂= 1 2 aligned C_ p C_ V &= n₁ C_ p₁ +n₂ C_ p₂ n₁ C_ V₁ +n₂ C_ V₂ &= 4 ( 3 2 +1 ) R+ 1 2 ( 5 2 +1 ) R 4 3 2 R+ 1 2 5 2 R &= (4 5 2 R )+ ( 1 2 7 2 R ) (4 3 2 R )+ ( 1