(a) Calculate the value of \(w\) for a system that releases \(216 \mathrm{~kJ}\) of heat in a process for which the decrease in internal energy is \(184 \mathrm{~kJ}\). (b) Is work done on or by the system during this process?

Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work. It defines macroscopic variables, such as internal energy, entropy, and pressure, that partly describe a body of matter or radiation. Thermodynamics deals with the transfer of energy from one place to another and from one form to another. The behavior of these quantities is governed by the laws of thermodynamics which apply universally.

One of the most fundamental concepts within thermodynamics is the system, which is the part of the universe we are focusing on, while the rest of the universe constitutes the surroundings. Systems can be isolated, closed, or open, depending on whether they exchange heat, matter, and work with their surroundings. For example, a boiling pot of water is an open system because it can exchange heat with its environment.

Understanding thermodynamics involves studying these exchanges and the principles that dictate the energy transformations involved, such as the conservation of energy principle. This is crucial not only in scientific endeavors but also in practical applications like engines, refrigerators, and many other machines that help shape our daily life.

Internal energy, denoted as U, represents the total energy contained within a system. It encompasses all forms of energy present, including kinetic energy due to the motion of atoms and molecules, and potential energy resulting from the forces among these particles. While we can measure the changes in internal energy, we cannot measure the total internal energy of a system directly.

The change in internal energy (\(\triangle U\)) can be calculated when a system undergoes a transition from one state to another. During any process, the change in internal energy is equal to the heat added to the system minus the work done by the system, as dictated by the first law of thermodynamics. This law suggests that energy cannot be created or destroyed in an isolated system, but can be transformed from one form to another.

Exercises to Grasp Internal Energy:

• Calculate the change in internal energy when a system absorbs heat or performs work.
• Analyze how internal energy changes during different thermodynamic processes, for example, during adiabatic or isothermal expansions and compressions.

In thermodynamics, work (\(W\)) and heat (\(Q\)) are two of the ways energy can be transferred into or out of a system. Work is done when a force is applied to a system resulting in displacement, while heat is transferred between systems due to a temperature difference.

When dealing with work, one should understand that it is signed: positive work is done on the system when the surroundings do work on it, and negative work is done by the system when it expands or releases energy. Correlatively, heat is also signed: positive when it is absorbed by the system, and negative when the system releases heat to the surroundings.

The first law of thermodynamics plays a pivotal role as it connects work, heat, and internal energy. According to this principle, if a system releases heat (a negative value of \(Q\)) and its internal energy decreases (a negative value of \(\Delta U\)), the work done by the system is found by the equation \(W = Q - \Delta U\). In the context of our exercise, releasing heat and decreasing internal energy both contribute to the system doing work on the surroundings.

Practical Implications:

• Understanding how refrigerators transfer heat against a temperature gradient, requiring work to be done on the system.
• Calculating the work done by steam in a piston during a phase of an engine's cycle, where work is often extracted from internal energy through heat transfer.