The internal energy of non-ideal gas depends on

Options

A. Temperature
B. Pressure
C. Volume
D. All of these

Answer

To determine the factors on which the internal energy of a non-ideal gas depends, we can analyze the contributions of kinetic and potential energy to the internal energy.

### Step-by-Step Solution:

1. **Understanding Internal Energy**:
The internal energy (U) of a gas is the sum of its kinetic energy (KE) and potential energy (PE). For a non-ideal gas, both kinetic and potential energies are relevant.

2. **Kinetic Energy Dependence**:
The kinetic energy of the gas molecules is primarily a function of temperature. As the temperature increases, the average kinetic energy of the molecules increases, leading to an increase in internal energy. Thus, we can say:
\[ KE \propto T \]
where T is the temperature.

3. **Potential Energy Dependence**:
The potential energy of the gas molecules depends on the intermolecular forces, which are influenced by the separation between the molecules. This separation is affected by the pressure and volume of the gas.
- If the volume increases (and pressure decreases), the separation between molecules increases, which generally leads to a decrease in potential energy.
- Conversely, if the volume decreases (and pressure increases), the separation decreases, which can lead to an increase in potential energy.

4. **Conclusion on Internal Energy**:
Since the internal energy is the sum of both kinetic and potential energies, and both of these energies depend on temperature, pressure, and volume, we conclude that:
\[ U \text{ depends on } T, P, \text{ and } V. \]

5. **Final Answer**:
Therefore, the internal energy of a non-ideal gas depends on all of these factors: temperature, pressure, and volume. The correct option is "all of these."