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Q.
In a container $3 \,mol$ of monoatomic gas and $2 \,mol$ of diatomic gas are mixed. What is the $C_{p} / C_{v}$ value of the gas mixture?
States of Matter
Solution:
$C_{ P _{\text {mix }}}=\frac{n_{ A } C_{ P _{ A }}+n_{ B } C_{ P _{ B }}}{\left(n_{ A }+n_{ B }\right)}=\frac{3 \times 5+2 \times 7}{(3+2)}=\frac{29}{5}$
$C_{ V _{\text {mix }}}=\frac{n_{ A } C_{V_{ A }}+n_{ B } C_{V_{ B }}}{\left(n_{ A }+n_{ B }\right)}=\frac{3 \times 3+2 \times 5}{3+2}=\frac{19}{5}$
$\therefore \frac{C_{ P _{\text {mix }}}}{C_{ V _{\text {mix }}}}=\frac{29}{19}$