In previous, Find the value of `gamma = C_(P) // C_(v) :`

Options

A. 1.6
B. 1.5
C. 1.6
D. 1.66

Explanation

To find the value of \( \gamma = \frac{C_P}{C_V} \) for a gaseous mixture containing 2.0 moles of oxygen (O2) and 3.0 moles of carbon dioxide (CO2), we will follow these steps:

### Step 1: Identify the values of \( C_P \) and \( C_V \) for each gas
- For oxygen (O2), \( C_P = 29 \, \text{J/(mol·K)} \) and \( C_V = 21 \, \text{J/(mol·K)} \).
- For carbon dioxide (CO2), \( C_P = 37 \, \text{J/(mol·K)} \) and \( C_V = 28 \, \text{J/(mol·K)} \).

### Step 2: Calculate \( \gamma \) for each gas
- For oxygen (O2):
\[ \gamma_{O2} = \frac{C_{P_{O2}}}{C_{V_{O2}}} = \frac{29}{21} \approx 1.38 \]
- For carbon dioxide (CO2):
\[ \gamma_{CO2} = \frac{C_{P_{CO2}}}{C_{V_{CO2}}} = \frac{37}{28} \approx 1.32 \]

### Step 3: Calculate the average \( \gamma \) for the mixture
To find the average \( \gamma \) for the mixture, we can use the mole fractions of each gas:
- Total moles \( n_{total} = 2 + 3 = 5 \)
- Mole fraction of O2:
\[ x_{O2} = \frac{2}{5} = 0.4 \]
- Mole fraction of CO2:
\[ x_{CO2} = \frac{3}{5} = 0.6 \]

Now, we can calculate the average \( \gamma \):
\[ \gamma_{mix} = x_{O2} \cdot \gamma_{O2} + x_{CO2} \cdot \gamma_{CO2} \]
Substituting the values:
\[ \gamma_{mix} = 0.4 \cdot 1.38 + 0.6 \cdot 1.32 \]
Calculating:
\[ \gamma_{mix} = 0.552 + 0.792 = 1.344 \]

### Final Answer
The value of \( \gamma \) for the gaseous mixture is approximately \( 1.344 \).

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