What is the specific heat ratio of diatomic gases ?

Answer

To find the specific heat ratio (γ) of diatomic gases, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Specific Heat Ratio (γ)**:
The specific heat ratio (γ) is defined as the ratio of the specific heat of a gas at constant pressure (C_p) to its specific heat at constant volume (C_v):
\[ \gamma = \frac{C_p}{C_v} \]

2. **Relate Specific Heat Ratio to Degree of Freedom**:
The specific heat ratio can also be expressed in terms of the degrees of freedom (f) of the gas:
\[ \gamma = 1 + \frac{2}{f} \]

3. **Identify the Degrees of Freedom for Diatomic Gases**:
For diatomic gases, the degrees of freedom (f) is typically 5. This includes:
- 2 translational degrees of freedom (movement in x and y directions)
- 2 rotational degrees of freedom (rotation about two axes)
- 1 vibrational degree of freedom (vibration along the bond)

4. **Substitute the Degrees of Freedom into the Equation**:
Now, substitute f = 5 into the equation for γ:
\[ \gamma = 1 + \frac{2}{5} \]

5. **Calculate the Value of γ**:
Simplifying the equation:
\[ \gamma = 1 + 0.4 = 1.4 \]

6. **Conclusion**:
Therefore, the specific heat ratio (γ) for diatomic gases is:
\[ \gamma = 1.40 \]

### Final Answer:
The specific heat ratio of diatomic gases is 1.40.

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