C

Step 1: Understanding Internal Energy of an Ideal Gas
For an ideal gas, the internal energy (U) is a function of temperature (T) only. This is because the internal energy is related to the kinetic energy of the gas molecules, which is directly proportional to the temperature.

Step 2: Role of Other Variables
- Specific Volume: While specific volume (v) can affect state properties, it does not directly influence internal energy for ideal gases since it's related to density and pressure.
- Pressure: Similar to specific volume, pressure (P) does not influence internal energy directly in the ideal gas model.
- Density: Density (ρ) is linked to specific volume and does not impact internal energy directly.

Conclusion: Therefore, the internal energy of an ideal gas depends solely on temperature.
Thus, the correct answer is C.