Final answer:
The internal energy of an ideal gas is dependent only on its temperature, not its volume or pressure. Thus, the assertion and reason provided are both correct, and the reason is the correct explanation of the assertion. The correct answer is option A.
Step-by-step explanation:
The internal energy of an ideal gas is a key concept in thermodynamics and is relevant to understanding how gases behave under different conditions. According to the kinetic theory of gases, the internal energy of an ideal gas is determined solely by its temperature. This is because the internal energy is a measure of the total kinetic energy of the gas molecules, which depends only on temperature and not on volume or pressure.
In the context of this question, the assertion is that the internal energy of an ideal gas does not depend upon the volume of the gas. This is indeed correct because the ideal gas law states that pressure, volume, and temperature are related in a way that the internal energy remains unchanged if the temperature is constant. Therefore, the reason given, stating that the internal energy of an ideal gas depends on the temperature of the gas, is also correct. This dependence on temperature is attributed to the fact that the average kinetic energy of the gas molecules, which constitutes the internal energy, is directly proportional to the absolute temperature.
An isothermal process is one where the temperature of the gas remains constant, and as such, there is no change in internal energy. This is different from an adiabatic process, where there is no heat exchange with the surroundings, but the internal energy can change as the gas does work or work is done on the gas.
When a gas expands adiabatically, work is done by the gas, reducing its internal energy unless external work is done to maintain the temperature, in which case the internal energy would remain constant.
The correct option is A: Both the assertion and the reason are correct, and the reason is the correct explanation of the assertion.