The change in the internal energy of a system can be expressed as the heat added to the system minus the work done by the system. This relationship can be mathematically formulated as:

where:

• $\Delta U$ represents the change in internal energy,
• $Q$ denotes the heat added to the system, and
• $W$ indicates the work done by the system.

When heat is added to a system, the internal energy increases. This occurs because the heat energy transferred to the particles within the system results in an increase in their motion, thereby elevating their kinetic energy.

Conversely, when work is performed by the system, the internal energy decreases. This happens because the work energy is transferred from the particles in the system to the surroundings, leading to a reduction in their kinetic energy and, consequently, a decrease in internal energy. In this scenario, the change in internal energy is represented by a negative value of $\Delta U$.

Thus, the change in internal energy of a system is intricately linked to the heat added and the work done. If the system absorbs more heat than the work it performs, the internal energy will increase. On the other hand, if the system performs more work than the heat it absorbs, the internal energy will decrease.