Calculate the degree of freedom of diatomic molecule?

Options

A. Non-steady flow
B. Compressible liquids
C. Streamlined flow
D. Turbulent flow

Answer

To calculate the degree of freedom of a diatomic molecule, we can follow these steps:

### Step 1: Understand the Concept of Degree of Freedom
The degree of freedom (f) of a molecule refers to the number of independent ways in which the molecule can move. For a diatomic molecule, we need to consider both translational and rotational motions.

### Step 2: Identify the Formula
The degree of freedom can be calculated using the formula:
\[ f = 3n - c \]
where:
- \( n \) is the number of molecules,
- \( c \) is the number of constraints.

### Step 3: Determine the Values of n and c
For a diatomic molecule:
- At high temperatures, the number of degrees of freedom due to translational and rotational motion is \( n = 2 \) (since it consists of two atoms).
- At high temperature, there are no constraints, so \( c = 0 \).

### Step 4: Calculate Degree of Freedom at High Temperature
Substituting the values into the formula:
\[ f = 3(2) - 0 = 6 \]
Thus, the degree of freedom at high temperature is 6.

### Step 5: Consider Low Temperature Conditions
At low temperatures, the number of degrees of freedom remains \( n = 2 \) (still a diatomic molecule), but there is a constraint due to the vibrational motion being frozen out. Here, \( c = 1 \).

### Step 6: Calculate Degree of Freedom at Low Temperature
Substituting the values into the formula:
\[ f = 3(2) - 1 = 5 \]
Thus, the degree of freedom at low temperature is 5.

### Conclusion
- Degree of freedom at high temperature: 6
- Degree of freedom at low temperature: 5