The ratio `gamma((C_(P))/(C_(V)))` for iner gases is

Options

A. 1.33
B. 1.66
C. 2.13
D. 1.99

Explanation

To find the ratio \( \gamma = \frac{C_P}{C_V} \) for inert gases, we can follow these steps:

### Step 1: Understand the specific heat capacities
For monoatomic gases (which include inert gases like argon, neon, and krypton), the specific heat capacities at constant volume \( C_V \) and at constant pressure \( C_P \) can be defined as follows:
- \( C_V = \frac{3R}{2} \)
- \( C_P = C_V + R \)

### Step 2: Calculate \( C_P \)
Using the equation for \( C_P \):
\[ C_P = C_V + R = \frac{3R}{2} + R \]
To add these, convert \( R \) into a fraction:
\[ R = \frac{2R}{2} \]
Now, substituting this into the equation:
\[ C_P = \frac{3R}{2} + \frac{2R}{2} = \frac{5R}{2} \]

### Step 3: Calculate the ratio \( \gamma \)
Now that we have both \( C_P \) and \( C_V \), we can find the ratio \( \gamma \):
\[ \gamma = \frac{C_P}{C_V} = \frac{\frac{5R}{2}}{\frac{3R}{2}} \]
The \( R \) and \( 2 \) in the numerator and denominator cancel out:
\[ \gamma = \frac{5}{3} \]

### Step 4: Convert to decimal form
To express this ratio in decimal form:
\[ \gamma = \frac{5}{3} \approx 1.66 \]

### Conclusion
Thus, the ratio \( \gamma = \frac{C_P}{C_V} \) for inert gases is \( \frac{5}{3} \) or approximately \( 1.66 \).