Question

A gaseous mixture consists of 16g of helium and 16g of oxygen. Then ratio Cp/Cv of mixture is :

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

Answer 1

The correct option is D 1.62

Given,

$M_{He}=4$, $m_{he}=16g$

$M_{ox}=32$, $m_{ox}=16g$

Specific heat of mixture at constant volume is given by,

$C_V=\frac{n_1{C}_{V_1}+n_2{C}_V{}_2}{n_1+n_2}$. . . . .(1)

For Helium gas,

No. of moles, $n_1=\frac{m_{he}}{M_{he}}$

$n_1=\frac{16}{4}=4$

${\gamma }_1=\frac{5}{3}$

Foe Oxygen Gas,

no. of moles, $n_2=\frac{m_{ox}}{M_{ox}}$

$n_2=\frac{16}{32}=\frac{1}{2}$

${\gamma }_2=\frac{7}{5}$

And specific heat constant volume of helium gas,

$C_V{}_1=\frac{R}{{\gamma }_1-1}=\frac{R}{\frac{5}{3}-1}=\frac{3}{2}R$

The specific heat of oxygen at constant volume,

$C_V{}_1=\frac{R}{{\gamma }_2-1}=\frac{R}{\frac{7}{5}-1}=\frac{5}{2}R$

From equation (1),

$C_V=\frac{4\times \frac{3}{2}R+\frac{1}{2}\times \frac{5}{2}R}{\frac{4}{1}+\frac{1}{2}}$

$C_V=\frac{29}{18}R=\frac{R}{\gamma -1}$

$\gamma =\frac{18}{29}+1$

$\frac{C_P}{C_V}=\gamma =1.62$

The correct option is D.