(a) Calculate the work for a system that releases \(346 \mathrm{~kJ}\) of heat in a process for which the decrease in internal energy is \(125 \mathrm{~kJ}\). (b) Is work done on or by the system during this process?

Thermodynamics is a branch of physics that deals with the relationships between heat, work, temperature, and energy within physical systems. At the core of thermodynamics are the laws that describe how energy moves and changes form. One of the fundamental principles of this discipline is the conservation of energy, meaning that within an isolated system, energy can be transformed but not created or destroyed. Understanding thermodynamics is essential not only in physics but also in engineering, chemistry, and biology because it helps explain how systems react to changes in their environment, such as temperature and pressure.

In many real-world applications, thermodynamics explains how engines work, how refrigerators cool, and even the principles that govern our weather. For students tackling homework in thermodynamics, the key lies in grasping how these physical quantities—heat, work, and internal energy—interact to lead to the observed behavior of systems.

Internal energy, often represented with the symbol 'U,' is the total energy contained within a system. This energy is the sum of the kinetic and potential energies of all the particles that make up the system. In a more tangible sense, internal energy could be seen as the energy required to create a system without adding any extra heat or work.

Changes in a system's internal energy can occur due to heat transfer or work done by or on the system. An increase in internal energy can result from either adding heat to the system or performing work on it, while a decrease can happen when the system releases heat or does work on the surroundings. It's crucial to recognize that while energy can be transferred in and out of a system, the internal energy itself is not something that can be directly measured—it can only be inferred by observing the system's response to changes in heat and work.

The concepts of work and heat are intimately related in thermodynamics. They are both forms of energy transfer between a system and its surroundings.

Heat

Heat, or 'Q', refers to energy transfer due to a temperature difference between the system and its environment. If the system gains heat, 'Q' is positive; if it loses heat, 'Q' is negative. This directional convention helps us understand the flow of heat energy.

Work

Work, or 'W', is the energy transfer when a force moves something over a distance. For example, when a gas expands in a cylinder, it does work on the piston. In thermodynamics, if the system does work on its surroundings, 'W' is considered positive. If work is done on the system, it's negative.

• These two forms of energy transfer are interconnected through the first law of thermodynamics, 'ΔU = Q + W'.
• Understanding the directional flow of heat and work is crucial in solving problems.
• The exercise provided exemplifies the principles of how heat release and work are accounted for when calculating the change in a system’s internal energy.

Grasping the interplay of work and heat allows students to not just solve mathematical problems, but also to comprehend the physical processes driving the changes in energy they calculate. In the referenced exercise, recognizing that work is positive when it is done by the system (heat released, in this case) is central to correctly applying the first law of thermodynamics and reaching a correct solution.