Question

A vessel contains 1 mol of o2 and 2 mol of he. what is the value of 'cp/cv' of the mixture?

Answer 1

molar specific heat capacity at constant volume , Cv is given by
$\bold{C_v=\frac{n_1C_{v_1}+n_2C_{v_2}}{n_1+n_2}}$
Here n₁ is the moles of O₂ and n₂ is moles of He also Cv₁ is molar specific heat capacity for O₂ and Cv₂ is molar specific heat capacity for He .
Given, n₁ = 1 , n₂ = 2
Cv₁ = 5R/2 [ because O₂ is diatomic ]
Cv₂ = 3R/2 [ because He is monoatomic ]
∴ Cv = (1 × 5R/2 + 2 × 3R/2)/(1 + 2) = (5R/2 + 6R/2)/3 = 11R/6

Similarly, Cp = (n₁Cp₁ + n₂Cp₂)/(n₁ + n₂)
Cp₁ = 7R/2 [ because O₂ is diatomic molecule]
Cp₂ = 5R/2 [ because He is monoatomic molecule]
Now, Cp = (1 × 7R/2 + 2 × 5R/2)/(1 + 2) = (7R/2 + 10R/2)/3 = 17R/6

Now, Cp/Cv = 17R/6/(11R/6) = 17/11