Adiabatic exponent of a gas is equal to

Options

A. `C_(P)xxC_(V)`
B. `(C_(P))/(C_(V))`
C. `C_(P)-C_(V)`
D. `C_(P)+C_(V)`

Answer

To determine the adiabatic exponent (γ) of a gas, we can follow these steps:

### Step 1: Understand the Definitions
- **Cp**: Heat capacity at constant pressure.
- **Cv**: Heat capacity at constant volume.
- **Adiabatic Exponent (γ)**: It is defined as the ratio of the heat capacities.

### Step 2: Write the Formula for Adiabatic Exponent
The adiabatic exponent (γ) is given by the formula:
\[ \gamma = \frac{C_p}{C_v} \]

### Step 3: Analyze the Options
Now, let's analyze the options provided in the question:
1. \(C_p \times C_v\) - This is incorrect as it does not represent a ratio.
2. \(\frac{C_p}{C_v}\) - This is correct as it matches the definition of the adiabatic exponent.
3. \(C_p - C_v\) - This is incorrect as it does not represent a ratio.
4. \(C_p + C_v\) - This is incorrect as it does not represent a ratio.

### Step 4: Conclusion
Based on the analysis, the correct answer is:
\[ \gamma = \frac{C_p}{C_v} \]