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The First Law of Thermodynamics is a fundamental principle which states that energy cannot be created or destroyed in an isolated system. It is often written as \[\begin{equation}\Delta U = Q - W\end{equation}\]where \(\Delta U\) is the change in internal energy of the system, \(Q\) is the heat added to the system, and \(W\) is the work done by the system on its surroundings. In the context of an ideal gas expanding at constant pressure, the work done by the gas (\(W_{\text{ew}}\)) is the force applied over distance, which translates to pressure times the change in volume (\[\begin{equation}W_{\text{ew}} = P \Delta V\end{equation}\]). Understanding the interplay between heat, work, and internal energy is crucial for interpreting physical processes and solving problems related to thermodynamics.Substituting the definition of work into the First Law allows you to relate heat transfer to the work done by the gas, offering a way to quantify how energy transfers occur in thermodynamic systems.

Internal Energy is a key concept in thermodynamics, referring to the total energy contained within a system, attributable to the kinetic and potential energy of the molecules. In the case of an ideal gas, the internal energy is primarily kinetic energy since the potential energy between non-interacting particles is negligible. The equation \[\begin{equation}\Delta U = \frac{3}{2} W_{\text{ew}}\end{equation}\]shows that the change in internal energy (\(\Delta U\)) for a monatomic ideal gas, which has three degrees of freedom, is related to the work done on the environment (\(W_{\text{ew}}\)). When the gas expands under constant pressure, it does work on the surroundings, and this work directly affects its internal energy. This equation gives us a quantitative measure of how the energy of a gas changes as it does work during an expansion or compression process.

Thermal Expansion of Gases is a concept that describes how gases change in volume in response to changes in temperature, assuming a constant pressure (known as Charles's Law). This is given by the equation \[\begin{equation}P \Delta V = nR \Delta T\end{equation}\]which is derived from the Ideal Gas Law. Here, \(\Delta V\) represents the change in volume, and \(\Delta T\) is the change in temperature in Kelvin. This behavior is crucial for understanding how gases will react in different situations, like when heat is added or removed. Thus, when a gas is heated, the increase in kinetic energy of the particles leads to an increase in volume if the pressure remains constant. Conversely, when a gas is cooled, its volume will decrease under the same conditions. The understanding of thermal expansion is significant in engineering applications and in real-life scenarios, such as when designing containers for gases that must withstand varying temperatures.