The internal energy of one mole of ideal gas is

Options

A. `3//2 RT`
B. `1//2 kT`
C. `1//2RT`
D. `3//2kT`

Explanation

To determine the internal energy of one mole of an ideal gas, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Internal Energy**:
- The internal energy (U) of an ideal gas is primarily due to the kinetic energy of its molecules since ideal gases are considered to have no intermolecular forces.

2. **Use the Formula for Internal Energy**:
- The internal energy of one mole of an ideal gas can be expressed using the formula:
\[ U = \frac{3}{2} nRT \]
- Here, \( n \) is the number of moles (which is 1 for one mole of gas), \( R \) is the universal gas constant (approximately 8.314 J/(mol·K)), and \( T \) is the absolute temperature in Kelvin.

3. **Substituting Values**:
- Since we are considering one mole of gas, we substitute \( n = 1 \):
\[ U = \frac{3}{2} \times 1 \times RT = \frac{3}{2} RT \]

4. **Conclusion**:
- Therefore, the internal energy of one mole of an ideal gas is given by:
\[ U = \frac{3}{2} RT \]

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

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