The internal energy of one mole of a gas is

Options

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

Explanation

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

### Step-by-Step Solution:

1. **Understanding Internal Energy**:
Internal energy (U) is a measure of the total energy contained within a system. For an ideal gas, the internal energy is primarily a function of temperature.

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

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

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 gas is \( \frac{3}{2} RT \).

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