Question

The ratio of specific heats $C_{p}/C_{v}$ for a mixture of 1 mole of helium and 1 mole of hydrogen is:

• A. 1.5
• B. 1.67
• C. 1.4
• D. 1.33

Hint:

For mixtures, always find the average $C_{v}$ first, then find $C_{p}$ and divide.

Answer 1

The Correct Option is A

Step 1: Concept
For a mixture of gases, the effective molar heat capacity at constant volume is $C_{v,mix} = \frac{n_{1}C_{v1} + n_{2}C_{v2}}{n_{1} + n_{2}}$.

Step 2: Meaning
Helium (He) is monatomic ($C_{v1} = \frac{3}{2}R$) and Hydrogen ($H_{2}$) is diatomic ($C_{v2} = \frac{5}{2}R$). Here $n_{1} = 1$ and $n_{2} = 1$.

Step 3: Analysis
$C_{v,mix} = \frac{1(1.5R) + 1(2.5R)}{2} = 2R$.
Using Mayer's relation $C_{p} - C_{v} = R$, we get $C_{p,mix} = 2R + R = 3R$.
The ratio $\gamma_{mix} = \frac{C_{p,mix}}{C_{v,mix}} = \frac{3R}{2R} = 1.5$.

Step 4: Conclusion
The ratio of specific heats for this equal-mole mixture is 1.5. Final Answer: (A)