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Internal energy is a measure of the energy stored within a system due to the motion and interactions of particles. In the context of an ideal monatomic gas like argon, the internal energy change when heat is added can be calculated using a specific formula: \( \Delta U = \frac{3}{2} n R \Delta T \). This formula represents the sum of the kinetic energies of all the molecules. Here, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(\Delta T\) is the change in temperature.
For such a monatomic gas, only translational kinetic energy (movement of particles through space) contributes to the internal energy. The atoms do not partake in rotating or vibrating in a way that affects this term because they are considered point masses. This is why you only see the \(\frac{3}{2}\) factor, which accounts for the three degrees of freedom each atom possesses.
To find the change in internal energy, you need to calculate the work done by the gas and use the relation from the first law of thermodynamics: \(Q = \Delta U + W\).
This tells us how much of the added heat goes into increasing the internal energy versus doing work on the surroundings.

The change in temperature \(\Delta T\) of a gas when heat is applied is a crucial factor that directly affects internal energy and, by extension, volume. For our argon gas, we can determine \(\Delta T\) using the rearranged first law of thermodynamics in combination with the formula for internal energy mentioned earlier.
Since we are assuming a constant pressure setting in this problem, the formula \( \Delta T = \frac{Q}{\frac{5}{2}nR} \) is used. This accounts for both the kinetic energy change and the work done as the gas expands, given the heat provided.
Plugging in:

• \(Q = 1800 \text{ J}\)
• \(n = 3.6 \text{ mol}\)
• \(R = 8.314 \text{ J/mol K}\)

you can solve for the resulting change in temperature.

Volume change in gases is closely linked to changes in temperature under constant pressure, as dictated by Charles's Law, which is a special case of the ideal gas law. The volume of a gas will expand or compress to maintain consistent pressure when temperature shifts.
To find this change in volume \(\Delta V\), the ideal gas law is rearranged to handle dynamics: \( \Delta V = \frac{nR \Delta T}{P} \). This relationship tells us how much the gas will expand when it's heated under a constant pressure of 120 kPa, considering our given values for \(R\), \(n\), and \(\Delta T\).
With the expansion, heat causes the particles in the gas to move faster, increasing pressure unless the volume increases proportionally. The volume changes to accommodate the new energy levels per the ideal gas computations.

A monatomic gas consists of single atoms that are not bonded to each other, like argon. This simplicity makes their thermodynamic model intuitive because it involves only straightforward motion without molecular rotations or vibrations.
For calculations involving heat and work, monatomic gases allow us to assume ideal behavior more easily. The system's energy changes can be conveniently analyzed using three degrees of freedom, as they modeled through straightforward kinetic terms.
Studies involving monatomic gases, particularly under ideal conditions, extrapolate to more complex systems but start with basic ideas like those related to internal energy and volume response to heating.

• Monatomic gases are robust models for applying ideal gas law concepts.
• Energetics remain basic due to their non-complicated structure.

Understanding monatomic gases paves the way for diving deeper into broader gas dynamics and thermodynamics by establishing clear foundational concepts.