$ abla U$

Definition

$ abla U$ represents the change in internal energy of a system. It is a fundamental concept in thermodynamics that describes the energy transferred between a system and its surroundings during a process, without consideration of the work done or heat exchanged.

5 Must Know Facts For Your Next Test

1. $ abla U$ is a state function, meaning it depends only on the initial and final states of the system and not the path taken to get there.
2. The change in internal energy, $ abla U$, is related to the work done on or by the system, $W$, and the heat added to or removed from the system, $Q$, through the First Law of Thermodynamics: $ abla U = Q - W$.
3. For a closed system, $ abla U$ is equal to the sum of the work done on the system and the heat added to the system, as there is no exchange of matter with the surroundings.
4. In the context of enthalpy, $ abla U$ represents the change in internal energy of a system during a process at constant pressure, and is related to the change in enthalpy, $ abla H$, through the equation: $ abla H = abla U + P abla V$.
5. The sign of $ abla U$ indicates whether the process is endothermic ($ abla U > 0$) or exothermic ($ abla U < 0$).

Review Questions

• Explain the relationship between $ abla U$ and the First Law of Thermodynamics.
  • According to the First Law of Thermodynamics, the change in a system's internal energy, $ abla U$, is equal to the sum of the work done on or by the system, $W$, and the heat added to or removed from the system, $Q$. This relationship is expressed mathematically as $ abla U = Q - W$. The First Law of Thermodynamics ensures that energy is neither created nor destroyed, but rather converted from one form to another, and $ abla U$ represents the net change in the system's internal energy during a process.
• Describe how $ abla U$ is related to the concept of enthalpy, $ abla H$.
  • In the context of enthalpy, the change in internal energy, $ abla U$, is related to the change in enthalpy, $ abla H$, through the equation $ abla H = abla U + P abla V$. Enthalpy represents the total energy of a system, including the internal energy and the work done due to changes in pressure and volume. The change in internal energy, $ abla U$, is a component of the overall change in enthalpy, which is a more comprehensive measure of the energy changes occurring within a system during a process at constant pressure.
• Analyze the significance of the sign of $ abla U$ in determining the nature of a process.
  • The sign of the change in internal energy, $ abla U$, indicates whether the process is endothermic or exothermic. If $ abla U$ is positive, the process is endothermic, meaning the system absorbs energy from the surroundings. Conversely, if $ abla U$ is negative, the process is exothermic, and the system releases energy to the surroundings. The sign of $ abla U$ provides valuable information about the energy changes occurring within the system and is an important consideration in understanding the thermodynamics of chemical and physical processes.

Related terms

Internal Energy: The total energy contained within a system, including the kinetic energy of the particles and the potential energy of their interactions.

First Law of Thermodynamics:

The principle that energy can be converted from one form to another, but cannot be created or destroyed, and the change in a system's internal energy is equal to the work done on the system plus the heat added to the system.

Enthalpy:

The sum of a system's internal energy and the work done by or on the system due to changes in pressure and volume, which represents the total energy of a system.