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In the context of gases, an isothermal process is one where the temperature remains constant throughout. "Iso" means "same," and "thermal" relates to heat, so the words combined refer to a constant temperature process. During isothermal expansion, a gas expands while keeping its temperature unchanged. This type of process is common when considering ideal gases - hypothetical gases that perfectly follow the ideal gas law.

For an ideal gas undergoing isothermal expansion:

• The energy added into the system is absorbed as work done by the gas, causing it to expand.
• There is no change in internal energy because the temperature doesn't change.
• According to the ideal gas equation, the product of pressure and volume remains constant with a constant temperature.

The equation underlying this isothermal change is:
\[ PV = ext{constant} \] This is derived from the ideal gas law, simplifying the expression whenever the temperature and number of moles of the gas remain constant during the change.

Pressure change in gases is an important aspect when dealing with physical changes and processes. In our scenario of an isothermal expansion, the pressure changes because of the direct relationship between pressure and volume in the gas law.

Starting with the ideal gas equation \(PV = nRT\):

• During the isothermal expansion, the volume of the gas doubles while the temperature stays the same.
• This doubling of volume leads to the halving of pressure to maintain the constant product of pressure and volume.

For example, if the initial pressure (\(P_1\)) is at a certain value with volume (\(V_1\)), and then the volume (\(V_2\)) becomes \(2V_1\) during expansion, the pressure (\(P_2\)) will become \(\frac{P_1}{2}\).

This showcases how the characteristics of the ideal gas are such that when the volume increases in an isothermal expansion, the pressure decreases to reinforce the constant state itemized by the equation.

Monatomic ideal gases are gases composed of single-atom molecules. Examples include helium, neon, and argon. These gases can be considered under the ideal gas law because they adhere closely to the assumptions inherent in this theoretical model. Understanding these gases helps in analyzing behaviors such as expansion and pressure changes.

For monatomic gases, these properties are noteworthy:

• They exhibit relatively simple behavior due to the lack of molecular bonds that could affect interactions.
• Their internal energy can be defined solely by their kinetic energy, which depends only on temperature.
• When undergoing processes like isothermal expansion, their behavior can be predicted accurately with the ideal gas law.

These fundamental characteristics make it comparatively straightforward to calculate results or predict outcomes when working under idealized conditions, allowing for simplifications that aid in learning and comprehension of basic thermodynamics concepts.