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# If 2 moles of diatomic gas and 1 mole of monoatomic gas are mixed , then ratio of specific heats $\;\large\frac{C_{p}}{C_{v}}\;$ is

$(a)\;\large\frac{7}{3}\qquad(b)\;\large\frac{5}{4}\qquad(c)\;\large\frac{19}{13}\qquad(d)\;\large\frac{15}{19}$

Answer : $\;\large\frac{19}{13}$
Explanation :
$C_{peq} = \large\frac{n_{1}C_{p_{1} }+ n_{2} C_{p_{2}}}{n_{1}+n_{2}}$
$C_{veq} = \large\frac{n_{1} C_{v_{1}}+n_{2} C_{v_{2}}}{n_{1}+n_{2}}$
$r_{eq} = \large\frac{C_{peq}}{C_{veq}} = \large\frac{\large\frac{2 \times \large\frac{7}{2}+1\times \large\frac{5}{2}}{3}}{2 \times \large\frac{5}{2} + 1 \times \large\frac{3}{2}}$
$=\large\frac{19}{13}$