Question

Consider a mixture of $n$ moles of helium gas and $2n$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $\frac{C_P}{C_v}$ value will be

• A. $\frac{19}{13}$
• B. $\frac{67}{45}$
• C. $\frac{40}{27}$
• D. $\frac{23}{15}$

Answer 1

The correct option is A $\frac{19}{13}$

Helium is a monoatomic gas and Oxygen is a diatomic gas.

$\text{For helium,}{C}_{V_1}=\frac{3}{2}R\text{and}{C}_{P_1}=\frac{5}{2}R$

$\text{For oxygen,}{C}_{V_2}=\frac{5}{2}R\text{and}{C}_{P_2}=\frac{7}{2}R$

For mixture,
$\gamma ={\left(\frac{C_P}{C_V}\right)}_{mixture}=\frac{N_1{C}_{P_1}+N_2{C}_{P_2}}{N_1{C}_{V_1}+N_2{C}_{V_2}}$

$\Rightarrow \gamma =\frac{n.\frac{5}{2}R+2n.\frac{7}{2}R}{n.\frac{3}{2}R+2n.\frac{5}{2}R}=\frac{19nR\times 2}{2\left(13nR\right)}$

$\therefore {\left(\frac{C_P}{C_V}\right)}_{mixture}=\frac{19}{13}$