Question

One mole of Ideal monatomic gas $(\gamma =\frac{5}{3})$ is mixed with one mole of diatomic gas $(\gamma =\frac{7}{5})$. What is $\gamma$ for the mixture?

• A. $\frac{3}{2}$
• B. $\frac{23}{15}$
• C. $\frac{35}{23}$
• D. $\frac{4}{3}$

Answer 1

Answer: (A)

$\frac{3}{2}$

Total no of moles: $\mu ={\mu }_1+{\mu }_2=1+1=2$

$C_v=\frac{R}{\gamma -1}$

$(C_v{)}_{mix}=\frac{\frac{{\mu }_{1}R}{{\gamma }_1-1}+\frac{{\mu }_{2}R}{{\gamma }_2-1}}{{\mu }_1+{\mu }_2}$

$C_p=\frac{R\gamma }{\gamma -1}$

$(C_p{)}_{mix}=\frac{\frac{{\mu }_{1}R{\gamma }_1}{{\gamma }_1-1}+\frac{{\mu }_{2}R{\gamma }_2}{{\gamma }_2-1}}{{\mu }_1+{\mu }_2}=$

${\gamma }_{mix}=\frac{2{\gamma }_1{\gamma }_2-{\gamma }_1-{\gamma }_2}{{\gamma }_1+{\gamma }_2-2}=\frac{2\times \frac{5}{3}\times \frac{7}{5}-\frac{5}{3}-\frac{7}{5}}{\frac{5}{3}+\frac{7}{5}-2}=\frac{\frac{24}{15}}{\frac{16}{15}}=\frac{3}{2}$