A vessel contains 1 mol of O2 and 2mol of He. what is the value of'Cp/Cv ' of the mixture?

Oxygen is diatomic, so its degree of freedom, (f1) = 5,

also its number of moles, n1 = 1

Helium is monoatomic, so its degree of freedom (f2) = 3

and its number of moles given is, n2=2

Now using formula of effective degree of freedom of mixture, (f), we have:

f = (f1n1+f2n2) / (n1+n2)

= (5*1 + 3*2) / (1+3)

=11/3

Also, from first law of thermodynamics;

U = n Cv. T = nRT (f2)

or, Cv = R. (f/2) (n & T cancel)

We know f=11/6,

substituting the value in above relation, we have:

Cv = R. 11/3*2

= R. 11/6

Also, Cp-Cv = R

or, Cp - R. (11/6) = R

or, Cp = R (11/6) + 1

= 17/6 R

Therefore, Cp/Cv = 17/11