The total internal energy of one mole of rigid diatomic gas is

Options

A. `(3)/(2)RT`
B. `(7)/(2)RT`
C. `(5)/(2)RT`
D. `(9)/(2)RT`

Explanation

To find the total internal energy of one mole of a rigid diatomic gas, we can follow these steps:

### Step 1: Understand the formula for internal energy
The internal energy (E) of a gas can be expressed using the formula:
\[ E = \frac{F}{2} nRT \]
where:
- \( F \) is the degrees of freedom,
- \( n \) is the number of moles,
- \( R \) is the universal gas constant, and
- \( T \) is the absolute temperature in Kelvin.

### Step 2: Identify the degrees of freedom for a diatomic gas
For a diatomic gas, the degrees of freedom (F) is typically 5. This includes:
- 3 translational degrees of freedom (movement in x, y, and z directions),
- 2 rotational degrees of freedom (rotation about two axes).

### Step 3: Substitute values into the formula
Since we are considering one mole of the gas (\( n = 1 \)), we can substitute \( F = 5 \) and \( n = 1 \) into the internal energy formula:
\[ E = \frac{5}{2} (1) RT \]
This simplifies to:
\[ E = \frac{5}{2} RT \]

### Step 4: Conclusion
Thus, the total internal energy of one mole of rigid diatomic gas is given by:
\[ E = \frac{5}{2} RT \]

### Final Answer
The total internal energy of one mole of rigid diatomic gas is \( \frac{5}{2} RT \).

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