Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium `M_(1) = 4g` and that of hydrogen `M_(2) = 2g`
The equivalent of `gamma` is

Options

A. `1.59`
B. `1.53`
C. `1.56`
D. None

Explanation

To find the equivalent of gamma (γ) for the mixture of helium and hydrogen, we will follow these steps:

### Step 1: Identify the specific heats for helium and hydrogen
- For helium (monatomic gas), the specific heat at constant pressure (C_p) is given by:
\[ C_{p, He} = \frac{7}{2} R \]
- For hydrogen (diatomic gas), the specific heat at constant pressure (C_p) is given by:
\[ C_{p, H_2} = \frac{7}{2} R \]

### Step 2: Calculate the total specific heat at constant pressure (C_p) for the mixture
- The total number of moles in the mixture is:
\[ n_{total} = n_{He} + n_{H_2} = 5 + 2 = 7 \text{ moles} \]
- The total specific heat at constant pressure (C_p) for the mixture can be calculated as:
\[ C_p = \frac{(n_{He} \cdot C_{p, He}) + (n_{H_2} \cdot C_{p, H_2})}{n_{total}} \]
Substituting the values:
\[ C_p = \frac{(5 \cdot \frac{7}{2} R) + (2 \cdot \frac{7}{2} R)}{7} \]
Simplifying this:
\[ C_p = \frac{(35R/2) + (14R/2)}{7} = \frac{49R/2}{7} = \frac{49R}{14} = \frac{7R}{2} \]

### Step 3: Calculate the specific heat at constant volume (C_v) for the mixture
- For helium, the specific heat at constant volume (C_v) is:
\[ C_{v, He} = \frac{5}{2} R \]
- For hydrogen, the specific heat at constant volume (C_v) is:
\[ C_{v, H_2} = \frac{5}{2} R \]
- The total specific heat at constant volume (C_v) for the mixture can be calculated as:
\[ C_v = \frac{(n_{He} \cdot C_{v, He}) + (n_{H_2} \cdot C_{v, H_2})}{n_{total}} \]
Substituting the values:
\[ C_v = \frac{(5 \cdot \frac{5}{2} R) + (2 \cdot \frac{5}{2} R)}{7} \]
Simplifying this:
\[ C_v = \frac{(25R/2) + (10R/2)}{7} = \frac{35R/2}{7} = \frac{35R}{14} = \frac{5R}{2} \]

### Step 4: Calculate gamma (γ)
- Gamma (γ) is defined as the ratio of specific heats:
\[ \gamma = \frac{C_p}{C_v} \]
Substituting the values we calculated:
\[ \gamma = \frac{\frac{7R}{2}}{\frac{5R}{2}} = \frac{7}{5} = 1.4 \]

### Conclusion
The equivalent of gamma (γ) for the mixture of helium and hydrogen is:
\[ \gamma = 1.4 \]