Concept: Internal energy of an ideal gas depends only on its temperature.

Why (A) is correct:

For an ideal gas, the internal energy ($U$) is solely a function of its absolute temperature ($T$). This is expressed as $U=n{C}_{v}T$, where $n$ is the number of moles and $C_v$ is the molar heat capacity at constant volume. The problem states that the ideal gas expands at a constant temperature. Since the temperature remains constant, the internal energy of the ideal gas also remains constant.

Option Analysis:

• A) Internal energy remains same: This is correct because for an ideal gas, internal energy is directly proportional to temperature, and the temperature is constant.
• B) Internal energy decreases: This would imply a decrease in temperature, which contradicts the given condition.
• C) Internal energy increases: This would imply an increase in temperature, which contradicts the given condition.
• D) Entropy first increases and then decreases: When an ideal gas expands, its entropy always increases because the system becomes more disordered. There is no condition under which it would first increase and then decrease during a simple expansion at constant temperature and pressure.

Correct Answer: (A)