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An isothermal process is a thermodynamic transformation in which a system's temperature remains constant. This implies that any heat energy entering or leaving the system does not change the system's internal temperature. In our exercise, a dilute gas expands while maintaining a steady temperature of 300 K.

What is compelling about an isothermal expansion, especially for an ideal gas, is that even though the gas does work and potentially absorbs heat, its internal energy remains unchanged. The reasoning behind this lies in the kinetic theory of gases, which states that the internal energy of an ideal gas is dependent solely on its temperature. Thus, even as a gas expands or compresses, if it does so isothermally, its internal energy does not vary.

To better understand this concept, imagine a gas trapped in a cylinder with a movable piston. The gas expands slowly against the piston, and heat is simultaneously supplied to the gas at such a rate that the temperature remains constant. The key takeaway for students is that an isothermal process, by definition, maintains a system's temperature, and for an ideal gas, this also means the internal energy stays the same.

Internal energy, designated as U, is the total energy contained within a thermodynamic system. It encompasses all forms of energy in the system, which for an ideal gas, relates mainly to the kinetic energy of its molecules. Since temperature is a measure of the average kinetic energy of the molecules in a substance, the internal energy in an ideal gas is directly proportional to its temperature.

In the context of our textbook exercise, the isothermal expansion of a gas has a fascinating implication: since the process occurs at a constant temperature, the internal energy does not change throughout the process. Mathematically, this is expressed as Δ±« = 0. This is a critical point for students to understand - during isothermal processes for an ideal gas, any work done by the gas or heat added to the gas does not result in a change in the gas' total internal energy.

Heat absorption in a thermodynamic process refers to the transfer of energy into a system in the form of heat. This process is denoted by the symbol Q. In our exercise, heat absorption is what allows the gas to do work on its surroundings during its expansion, while sticking to an isothermal condition.

Using the First Law of Thermodynamics, which states that the change in internal energy of a system (Δ±«) is equal to the heat added to the system (Q) minus the work done by the system (W), and considering that Δ±« is zero for an isothermal process, we can deduce that the heat absorbed by the gas is equal to the work done by it, Q = W. In the case of the exercise, the gas absorbs 250 Joules of heat.

It is also important for learners to understand that heat transfer can occur in various ways, such as conduction, convection, and radiation. In an isothermal process of an ideal gas, all of the heat absorbed goes into doing work and none into changing the internal energy of the system, due to the constancy of temperature.