Question

If 8 grams of helium is mixed with 32 grams of oxygen then ratio of CP by CV is

Answer 1

Given :

Mass of helium = 8 gm

Mass of oxygen = 32 gm

To Find :

$\frac{C_p}{C_v}$  ratio

Solution :

Number of moles of helium (n) = $\frac{8}{4}$  = 2 moles

Number of moles of oxygen (n') = $\frac{32}{32}$ = 1 mole

For Helium atom, C$_v$ = $\frac{3}{2}$R

For Oxygen atom, C'$_v$ = $\frac{5}{2}$R

C$_v$ of the mixture = $\frac{nC_v + n'C'_v}{n + n'}$  

                             = $\frac{2*\frac{3}{2}R + 1*\frac{5}{2}R }{2 + 1}$

                             =  $\frac{3R+ \frac{5}{2}R }{3}$

                             =  $\frac{11R}{2*3}$

                             =   $\frac{11R}{6}$

γ of the mixture = $\frac{C_p}{C_v}$

                          = 1 + $\frac{R}{C_v (mix)}$

                          = 1 + $\frac{6R}{11R}$

                          = $\frac{17}{11}$

Therefore, $\frac{C_p}{C_v}$ i.e, γ of the mixture is $\frac{17}{11}$.