Select the correct statement : (a) internal energy of a real gas at a given temperature increases as the volume increases (b) internal energy of an ideal gas at given temperature increase as the volume increases (c) internal energy of an ideal gas molecules is not a function of temperature (d) the internal energy of a real gas at a constant temperature is independent of change in volume

When we discuss the properties of an ideal gas, we're referring to a theoretical model used in physics and chemistry to simplify the study of gases. According to this model, ideal gases have several specific properties: the particles are considered point masses with no volume, they are in constant, random, straight-line motion, and collisions between them are perfectly elastic. Moreover, an important aspect is that the particles do not exert any forces on each other, whether it's attractions or repulsions.

These assumptions lead to the conclusion that, for an ideal gas, the internal energy—which is the total energy of the gas particles' motion—is solely dependent on the temperature. A change in volume at a constant temperature will not affect its internal energy. This concept is elemental in understanding statement (b) from the exercise provided, which is an incorrect assertion for an ideal gas.

The Kinetic Molecular Theory (KMT) is a model that explains the behavior of gas molecules. It posits that gas particles are in constant motion and that the temperature of the gas is a measure of the average kinetic energy of these particles. According to KMT, as the temperature increases, the particles move faster because their kinetic energy increases.

It's important to note that KMT is the foundation for understanding why the internal energy of ideal gas is a function of temperature, as mentioned in statement (c), which is a false claim. In ideal gases, as long as the temperature remains unchanged, regardless of how the volume or pressure might alter, the internal energy stays constant because it's derived from the particles' kinetic energy.

In contrast to ideal gases, real gases exhibit more complex behavior. Real gas particles occupy space and do interact with one another through van der Waals forces (attractive and repulsive forces). These factors become particularly significant at high pressures, low temperatures, or when the gas particles are very polarizable. As these conditions stray from the ideal, the behavior of the gas changes and becomes more difficult to predict with simple models.

Contrary to ideal gases, the internal energy of real gases can depend on volume because of these intermolecular interactions. This is why statement (a) has the potential to be true, and statement (d) is indeed the correct answer, though it assumes the volume change does not lead to a phase change or significant alteration in particle interactions.

The study of thermodynamics deals with the relationships between heat, energy, and work. It encompasses principles that apply to systems in equilibrium and is governed by laws that describe how energy is transferred and how it affects matter. One of the core concepts of thermodynamics is that energy cannot be created or destroyed, only converted from one form to another.

The internal energy is a central term in thermodynamics and is considered a state function, meaning it only depends on the current state of the system (defined by variables like temperature and volume) and not on how the system got to that state. For ideal gases, thermodynamics supports the notion that their internal energy change is primarily a function of temperature change, not volume or pressure change. This provides further clarity on why statement (b) in the exercise was incorrect for an ideal gas scenario.