Question
The ratio $$\frac{{{C_P}}}{{{C_V}}}$$ for a gas mixture consisting of $$8\,g$$ of helium and $$16\,g$$ of oxygen is
A.
$$\frac{{24.2}}{{15}}$$
B.
$$\frac{{15}}{{23}}$$
C.
$$\frac{{27}}{{17}}$$
D.
$$\frac{{17}}{{27}}$$
Answer :
$$\frac{{24.2}}{{15}}$$
Solution :
$$\gamma \,\,{\text{for}}\,\,He = \frac{5}{3};\gamma \,\,{\text{for}}\,\,{O_2} = \frac{7}{5}$$
$$8\,g$$ of $$He$$ is equal to $$2\,moles$$ of $$He$$ and $$16\,g$$ of $${O_2} = \frac{1}{2}$$ $$mole$$ of $${O_2}$$ gas. Total one has $$2\frac{1}{2}\,moles.$$
$$\therefore $$ The weighted average is
$$\eqalign{
& = \left( {2 \times \frac{5}{3} + \frac{7}{5} \times \frac{1}{2}} \right) \times \frac{2}{5} = \left\{ {\frac{{10}}{3} + \frac{7}{{10}}} \right\} \times \frac{2}{5} \cr
& = \frac{{121}}{{30}} \times \frac{2}{5} = \frac{{24.2}}{{15}} \cr} $$