For a certain reaction at constant pressure, \(\Delta H=-15 \mathrm{~kJ}\), and \(22 \mathrm{~kJ}\) of expansion work is done on the system. What is \(\Delta U\) for this process?

The concept of internal energy is central to understanding thermodynamics and specifically the behavior of systems undergoing various processes. Internal energy, often denoted as \(U\), encapsulates the total energy held by a system's particles, comprising both kinetic and potential energies. These can include the motion of molecules (translational, rotational, vibrational) and intermolecular forces. Thus, changes in a system’s temperature or phase signal a shift in internal energy, although this change is not always apparent externally.

The First Law of Thermodynamics intimates the conservation of energy within an isolated system, indicating that internal energy can change by either adding or removing heat (\(q\)), or by doing work (\(w\)) on or by the system. Mathematically, we express this interaction with the formula: \[\Delta U = q + w\]. Understanding internal energy is paramount as it helps us evaluate how systems will behave when subjected to different thermodynamic processes.

Enthalpy change, denoted as \(\Delta H\), is a crucial concept, primarily when evaluating processes at constant pressure, which is common in chemistry and the study of reactions. Enthalpy is the measure of total heat content in a system, linked to internal energy (\(U\)) plus the product of pressure (\(P\)) and volume (\(V\)): \(H = U + PV\).

The change in enthalpy during a process signals whether heat was absorbed or released. A negative \(\Delta H\) indicates exothermic reactions, where heat is expulsed, making the surroundings warmer. Conversely, a positive \(\Delta H\) suggests endothermic reactions absorbing heat, thus cooling the vicinity. In the context of the provided exercise, the reaction's \(\Delta H = -15 \mathrm{~kJ}\) signifies an exothermic reaction. It is also worth noting that under constant pressure, enthalpy change is equal to the heat transferred (\(q_p\)), fundamentally linking this concept to the first law of thermodynamics.

Thermodynamics is a broad and foundational field of physics that studies the relationship between various forms of energy and work. It revolves around concepts such as internal energy, work, heat, and the fundamental laws that govern these interactions in systems. Importantly, the First Law of Thermodynamics establishes the conservation of energy, implying that energy can neither be created nor destroyed, only transformed. Additionally, this law asserts the connection between internal energy change (\(\Delta U\)), heat (\(q\)), and work (\(w\)) as \[\Delta U = q + w\].

Thermodynamics guides us in predicting how energy transfers and transformations initiate changes within a system. For students and professionals across various disciplines like chemistry, engineering, and environmental science, mastery of thermodynamics is essential for analyzing and designing processes and systems.

Examination of processes at constant pressure is particularly relevant in thermodynamics, where pressure \(P\) is one of the defining parameters of a system’s state. Constant pressure conditions are typical in many real-world scenarios, like chemical reactions taking place in open-atmosphere laboratory settings.

At constant pressure, work done on or by the system can be calculated by \(w = -P\Delta V\), where \(\Delta V\) represents the change in volume. Furthermore, the concept of enthalpy (\(H\)) becomes especially useful under these conditions since enthalpy change (\(\Delta H\)) mirrors the heat transferred at constant pressure. This direct relationship allows for simplification when applying the First Law of Thermodynamics, as in the exercise where the enthalpy change gives us the amount of heat involved in the reaction, and it's possible to calculate the change in internal energy. When the pressure is constant, it's easier to measure changes and understand the system's energy flow without needing to account for potential pressure variations.