Question

Three moles of oxygen are mixed with two moles of helium. What will be the ratio of specific heats at constant pressure and constant volume for the mixture?

• A. $2.5$
• B. $3.5$
• C. $1.5$
• D. $1$

Answer 1

Answer: (C)

For a monatomic gas like helium ${\gamma }_{He}=\frac{5}{3}$
For a diatomic gas like oxygen ${\gamma }_{O_2}=\frac{7}{5}$
$\therefore {\gamma }_{mix}=\frac{3\times {\gamma }_{O_2}+2\times {\gamma }_{He}}{\left(3+2\right)}$
$=\frac{3\times \frac{7}{5}+2\times \frac{5}{3}}{5}=\frac{\frac{21}{5}+\frac{10}{3}}{5}=\frac{113}{15\times 5}=1.5$