Question

If two moles of diatomic gas and one mole of monoatomic gas are mixed, then the ratio of specific heats is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

${\mu }_1=1,{\gamma }_1=\frac{5}{3}$(for monoatomic gas) and ${\mu }_2=2,{\gamma }_2=\frac{7}{5}$(for diatomic gas)
${\gamma }_{mixture}=\frac{\frac{{\mu }_1{\gamma }_1}{{\gamma }_1-1}+\frac{{\mu }_2{\gamma }_2}{{\gamma }_2-1}}{\frac{{\mu }_1}{{\gamma }_1-1}+\frac{{\mu }_2}{{\gamma }_2-1}}=\frac{\frac{1\times \frac{5}{3}}{\frac{5}{3}-1}+\frac{2\times \frac{7}{5}}{\frac{7}{5}-1}}{\frac{1}{\frac{5}{3}-1}+\frac{2}{\frac{7}{5}-1}}=\frac{5/2+7}{3/2+5}=\frac{19}{13}$