The internal energy of one mole mono-atomic gas is

Options

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

Explanation

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

### Step-by-Step Solution:

1. **Understand the Formula for Internal Energy**:
The internal energy (U) of n moles of an ideal gas is given by the formula:
\[ U = \frac{F}{2} nRT \]
where:
- \( U \) is the internal energy,
- \( F \) is the degrees of freedom of the gas,
- \( n \) is the number of moles,
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature in Kelvin.

2. **Identify the Degrees of Freedom for Monoatomic Gas**:
For a monoatomic gas, the degrees of freedom \( F \) is equal to 3. This is because monoatomic gases have three translational degrees of freedom (movement in x, y, and z directions).

3. **Substitute the Values into the Formula**:
Since we are dealing with one mole of gas, we set \( n = 1 \). Now substituting the values into the internal energy formula:
\[ U = \frac{3}{2} \times 1 \times R \times T \]

4. **Simplify the Expression**:
This simplifies to:
\[ U = \frac{3}{2} RT \]

5. **Final Result**:
Therefore, the internal energy of one mole of a monoatomic gas is:
\[ U = \frac{3}{2} RT \]

### Final Answer:
The internal energy of one mole of a monoatomic gas is \( \frac{3}{2} RT \).

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