Question

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

Answer 1

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