c
For \(N _{2},\) degree of freedom, \(f=5\)

For Ar, degree of freedom, \(f=3\)

Gas	\(C_V\)	\(C_p\)	Moles
\(N _{2}\)	\(\frac{5}{2} R\)	\(\frac{7}{2} R\)	\(1 / 4\)
Ar	\(\frac{3}{2} R\)	\(\frac{5}{2} R\)	\(1 / 4\)

The specific heat of the mixture at constant pressure is,

\(C_{\text {Pmix}}=\frac{n_{1} C_{P 1}+n_{2} C_{P 2}}{n_{1}+n_{2}}\)

\(=\frac{\frac{1}{4} \times \frac{7}{2} R+\frac{1}{2} \times \frac{5}{8} R}{\frac{1}{4}+\frac{1}{2}}\)

\(=\frac{17 R}{6}\)

The specific heat of the mixture at constant volume is,

\(C_{V_{\operatorname{mix}}}=\frac{n_{1} C_{V_{1}}+n_{2} C_{V_{2}}}{n_{1}+n_{2}}\)

\(=\frac{\frac{1}{4} \times \frac{5}{2} R+\frac{1}{2} \times \frac{3}{8} R}{\frac{1}{4}+\frac{1}{2}}\)

\(=\frac{11 R}{6}\)

The ratio \(C_{p} / C_{V}\) of the mixture is,

\(\left(\frac{C_{P}}{C_{V}}\right)_{\operatorname{mix}}=\frac{17}{11}\)