According to Joule's Second Law, what does the internal energy of an ideal gas depend on?

The internal energy of an ideal gas is fundamentally dependent on its temperature. This relationship stems from the kinetic theory of gases, which asserts that the internal energy of an ideal gas is a function of the average kinetic energy of its molecules. As the temperature increases, the average kinetic energy of the gas molecules also increases, which consequently raises the internal energy.

In contrast, the internal energy of an ideal gas does not depend on pressure, volume, or mass for a fixed amount of gas at a constant temperature. Changes in pressure or volume occur without changing the internal energy of an ideal gas, as long as the temperature remains constant. Therefore, even if the volume or pressure of the gas changes, these factors do not influence the internal energy directly. Additionally, while mass does affect the total internal energy (since it relates to the number of particles), the term 'internal energy' is usually considered per mole or per unit amount of substance and is primarily influenced by temperature.

This highlights the key concept that in ideal gases, the internal energy is solely a function of temperature, making it vital to understand the relation for applications in thermodynamics.