The degrees of freedom of a triatomic gas is

Options

A. 6
B. 4
C. 2
D. 8

Answer

To find the degrees of freedom of a triatomic gas, we can follow these steps:

### Step 1: Understand the formula for degrees of freedom
The degrees of freedom (F) of a gas can be calculated using the formula:
\[ F = 3n - k \]
where:
- \( n \) is the number of particles (atoms in this case),
- \( k \) is the number of constraints.

### Step 2: Identify the number of particles for a triatomic gas
A triatomic gas consists of molecules that contain three atoms. Therefore, for a triatomic gas:
\[ n = 3 \]

### Step 3: Determine the number of constraints
For a triatomic gas, there are typically three constraints due to the fact that the molecules can rotate and vibrate in three dimensions. Thus, we have:
\[ k = 3 \]

### Step 4: Substitute the values into the formula
Now we can substitute the values of \( n \) and \( k \) into the degrees of freedom formula:
\[ F = 3(3) - 3 \]

### Step 5: Calculate the degrees of freedom
Now, we perform the calculation:
\[ F = 9 - 3 = 6 \]

### Conclusion
The degrees of freedom of a triatomic gas is:
\[ \text{Degrees of freedom} = 6 \]

Thus, the correct answer is 6.

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