A gas sample in a piston assembly expands, doing \(536 \mathrm{~kJ}\) of work on its surroundings at the same time that \(214 \mathrm{~kJ}\) of heat is added to the gas. (a) What is the change in internal energy of the gas during this process? (b) Will the pressure of the gas be higher or lower when these changes are completed?

Internal energy is a fundamental concept in thermodynamics, representing the total energy contained within a system, which may consist of the kinetic energy due to the motion of molecules, and potential energy arising from intermolecular forces. When studying the behavior of gases, internal energy is crucial because it influences temperature, pressure, and volume of the gas.

Let’s consider the piston assembly example. The change in internal energy, signified as \(\Delta U\), includes all forms of energy transfers, such as heat and work. When heat is added to the gas, the internal energy increases, and when the gas does work on its surroundings by expanding, the internal energy decreases. A negative \(\Delta U\) indicates that the energy of the gas is reduced after the process. This reduction could lead to a decrease in temperature, as heat is a form of energy transfer that increases molecular motion and thus the internal energy.

Understanding internal energy is key for interpreting more than just temperature changes. This concept is integral to predicting the behavior of substances in various thermodynamic processes and scenarios.

Thermodynamics is the science that deals with heat, work, and the forms of energy involved in chemical or physical processes. It is based on several fundamental laws, with the first law of thermodynamics addressing energy conservation in systems. The principle works on the premise that energy can be transferred or transformed but not created or destroyed.

In any thermodynamic process, especially in cases like our piston assembly, multiple forms of energy interact. The first law helps us assess the system's energy change by accounting for both heat transfer and work done. The role of heat in this context is particularly significant because it represents energy in transit—often as a result of a temperature difference—and can change the internal energy and thus the state of the system. Work, on the other hand, represents a transfer of energy when an external force is applied over a distance, such as the gas pushing against the piston.

Unraveling the interplay between heat, work, and internal energy allows for a comprehensive understanding of the processes governing the behavior and equilibrium of systems, which is what thermodynamics seeks to achieve.

When discussing work and heat in thermodynamics, we often refer to them as two distinct paths for energy transfer into or out of a system. In our piston example, the gas does work on the surroundings by expanding against a force, and heat is simultaneously added to the system.

• Work (\(W\)): The process by which energy is exchanged due to a force causing displacement. If a gas expands, it does positive work on its surroundings, and if compressed, the work done on the gas is positive, increasing its internal energy.
• Heat (\(Q\)): It is the form of energy transfer driven by a temperature difference. Adding heat to a system increases its internal energy unless it is utilized for performing work.

Interrelation of Work and Heat

Heat and work are related through the first law of thermodynamics: \(\Delta U = Q - W\). This equation is a statement of energy conservation. If more work is done by the system than the heat added to it, the internal energy decreases, resulting in potential changes in temperature and pressure, as seen with the gas in the piston.

Understanding how these two modes of energy transfer interplay provides a clearer picture regarding the outcome of thermodynamic processes. It’s no wonder that students are often advised to treat these concepts with diligence to fully appreciate the broad implications they hold in the field of thermodynamics.