Question

A gaseous mixture consists of 4 g of oxygen and 4 g of helium. The ratio \( \frac{C_p}{C_v} \) of the mixture is

• A. \( \frac{13}{9} \)
• B. \( \frac{47}{29} \)
• C. \( \frac{47}{18} \)
• D. \( \frac{29}{13} \)

Hint:

Always use mole-fraction weighted averages for thermodynamic properties in gas mixtures.
Remember: For monoatomic gases \( \gamma = \frac{5}{3} \), for diatomic gases \( \gamma = \frac{7}{5} \).

Answer 1

The Correct Option is B

First calculate moles: \[ \text{O}_2: \frac{4}{32} = 0.125\ \text{mol}, \quad \text{He}: \frac{4}{4} = 1\ \text{mol} \] Specific heats: \[ \text{O}_2: C_v = \frac{5}{2}R, \quad C_p = \frac{7}{2}R \quad \text{He}: C_v = \frac{3}{2}R, \quad C_p = \frac{5}{2}R \] Total: \[ C_v = 0.125 \cdot \frac{5}{2}R + 1 \cdot \frac{3}{2}R = \frac{29}{8}R,\quad C_p = 0.125 \cdot \frac{7}{2}R + 1 \cdot \frac{5}{2}R = \frac{47}{8}R \] \[ \Rightarrow \frac{C_p}{C_v} = \frac{47}{29} \]