What will be the change in internal energy when 12 kJ of work is done on the system and 2 kJ of heat is given by the system? (a) \(+10 \mathrm{~kJ}\) (b) \(-10 \mathrm{~kJ}\) (c) +5kJ (d) \(-5 \mathrm{~kJ}\)

When discussing the concepts underlying the First Law of Thermodynamics, a fundamental term that needs to be understood is internal energy. This refers to the total energy contained within a system, arising from the kinetic and potential energies of the particles that make up the system, such as atoms and molecules.

Internal energy can change when a system exchanges heat or work with its surroundings. In the context of the solution provided, when work is done on the system, it contributes to an increase in the internal energy, whereas if the system does work on its surroundings, it would decrease the internal energy. Similarly, when heat is absorbed by the system, the internal energy increases, and when heat is released, it decreases.

It's crucial to consider both heat and work when assessing changes in internal energy, as they are the two primary ways energy is transferred into or out of the system. The exercise emphasizes that despite work being done on the system and heat being released by it, internal energy can still increase, highlighting the interplay between these two energy transfer methods.

Moving onto the broader concept of thermodynamics, this field of physics explores the relationships between heat, work, temperature, and energy. The First Law of Thermodynamics, central to the exercise you're studying, is one of the foundational principles in this area. It asserts that energy cannot be created or destroyed, but only transformed from one form to another, which corresponds with the law of conservation of energy.

In practical terms, this law implies that the change in the internal energy of a closed system is equal to the heat exchanged with its surroundings minus the work done by the system on its surroundings. As seen in the exercise, applying the First Law allows for the calculation of the internal energy change during processes where heat and work interactions occur.

Understanding thermodynamics is crucial not only in physics but also in engineering, chemistry, and even meteorology, as it provides essential insights into energy conversion and the efficiency of systems.

Lastly, highlighting the role of work and heat in thermodynamics is vital for a deep understanding of the First Law. Work in thermodynamics refers to the energy transferred when an external force causes a displacement. Conversely, heat is the energy transfer accountable to a temperature difference between the system and its surroundings.

In the context of the exercise provided, when work is done on the system, this increases its internal energy. However, the reverse occurs when the system does work: its internal energy decreases. This interaction with heat leads to a dynamic where the internal energy of a system can be affected by multiple simultaneous processes.

Ultimately, the crux of thermodynamics lies in these energy exchanges, and mastering them allows us to understand how different processes can alter the energy content of a system. With the exercise we've looked at, it's clear that both the work done and the heat exchanged contribute critically to determining the system's energetic outcome.