Question

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $Cp/Cv$ of the mixture is

• A. 1.4
• B. 1.54
• C. 1.59
• D. 1.62.

Answer 1

Answer: (D)

Using $C_{v_{mix}}=\frac{n_0{C}_{v_0}+n_H{C}_{v_H}}{n_0+n_H}$ and $C_{p_{mix}}=\frac{n_0{C}_{p_0}+n_H{C}_{p_H}}{n_0+n_H}$ Also $C_v=\frac{f}{2}R$ and $C_p=\left(1+\frac{n}{2}\right)R$ For oxygen, $n_0=\frac{1}{2}$ and $f_0$ = 5 ; for helium $n_H$ = 4 and $f_H$ = 3, then $\frac{C_p}{C_v}=\frac{4\times \frac{5}{2}R+\frac{1}{2}\times \frac{7}{2}R}{4\times \frac{3}{2}R+\frac{1}{2}\times \frac{5}{2}R}$