Internal energy is the sum of the kinetic and potential energies of the particles within a system. For a perfect gas, the internal energy depends on the following factors:

Temperature: The internal energy of a gas is directly proportional to its temperature. As the temperature increases, the average kinetic energy of the gas particles also increases, resulting in a higher internal energy.

Specific heat: The specific heat is the amount of heat energy required to raise the temperature of a substance by a certain amount. It is a characteristic property of a substance. The specific heat determines how much heat energy is needed to change the internal energy of a gas. Different gases have different specific heats, so the internal energy will depend on the specific heat of the gas.

Entropy: Entropy is a measure of the disorder or randomness in a system. It is related to the number of possible microstates that a system can occupy. The internal energy of a gas is related to its entropy. An increase in entropy leads to an increase in the internal energy of the gas.

Pressure: The pressure of a gas is a measure of the force exerted by the gas on its surroundings. It is related to the average kinetic energy of the gas particles. However, in the case of a perfect gas, the internal energy depends only on the temperature and not on the pressure. This is because a perfect gas obeys the ideal gas law, which states that the pressure and volume of a gas are inversely proportional at constant temperature. Therefore, a change in pressure does not result in a change in internal energy for a perfect gas.

In conclusion, the internal energy of a perfect gas depends primarily on the temperature. While specific heat and entropy can also influence the internal energy, the pressure does not have a direct effect on the internal energy of a perfect gas.