A system changes from state \(X\) to \(Y\) with a change in internal energy measuring to \(25 \mathrm{k}] \mathrm{mol}^{-1}\), by a reversible path and returns from \(Y\) to \(X\) by an irreversible path. What will be the net change in internal energy? (a) \(25 \mathrm{~kJ}\) (b) \(>25 \mathrm{~kJ}\) \((c)<25 \mathrm{k}]\) (d) zero

Thermodynamics is a foundational concept in physics that deals with the study of energy, work, and heat, and how they intersect and transform within different systems. At its core, thermodynamics seeks to understand how energy is transferred from one form to another and how it affects matter on a macroscopic scale.

It operates on several key principles, known as the laws of thermodynamics. The first law, for instance, asserts the conservation of energy within a closed system – energy can neither be created nor destroyed, only transformed or transferred. The second law introduces the concept of entropy, indicating that systems tend to progress towards a state of disorder or randomness.

Understanding the principles of thermodynamics is crucial for various applications across engineering, chemistry, and even biological systems, as it helps to predict the direction of energy flow and the efficiency of energy conversion processes.

Reversible and irreversible processes are two contrasting concepts in thermodynamics that describe how systems change state. A reversible process is an idealized or theoretical scenario where a system changes state in such a way that the system and its surroundings can be restored to their original states without any net change in the universe. These processes proceed infinitesimally slowly and are characterized by an equilibrium at every stage.

An irreversible process, on the other hand, is more common in reality. It occurs spontaneously and cannot be undone without leaving a net change in the universe. Irreversible processes involve dissipative effects like friction, turbulence, and inelastic deformation, leading to an increase in entropy.

In practical terms, most processes in nature are irreversible, contributing to the natural progression towards disorder. However, reversible processes are important theoretical models that help scientists understand the maximum efficiency that can be achieved under idealized conditions.

The conservation of energy principle is a cornerstone of physics, encapsulated in the first law of thermodynamics. It states that energy cannot be created or destroyed in an isolated system; it can only change from one form to another. The total amount of energy remains constant over time. In terms of internal energy, this principle implies that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings.

Mathematically, this can be expressed as \(\text{Change in internal energy (\(\text{Δ}U\))} = \text{Heat added (\(\text{Q}\))} - \text{Work done by the system (\(\text{W}\))}\). The application of this principle allows us to solve various problems in thermodynamics, such as calculating the net energy transfer in mechanical and thermal processes. In the context of the exercise, despite the path taken (reversible or irreversible), the conservation of energy dictates that the system's internal energy returns to its original value when the system returns to its initial state.