Final answer:
In an ideal isothermal system with ideal gases, the internal energy (dU) is zero because the temperature of the system, which determines the internal energy of an ideal gas, remains constant in an isothermal process.
Step-by-step explanation:
The internal energy (dU) of an ideal gas in an isothermal process is constant, meaning it does not change. In an isothermal process, the temperature of the system remains constant, and by definition, the internal energy of an ideal gas depends only on temperature. Since the temperature is constant, the internal energy change (dU) is zero, making option (a) Zero the correct answer.
Per the first law of thermodynamics, which expresses the principle of conservation of energy, any heat added to the system (Q) in an isothermal process is used to do work (W) by the system. Mathematically, this relationship is represented as ΔEint = Q - W for a process, where ΔEint represents the change in internal energy. For an isothermal process, this equation simplifies to ΔEint = 0 because Q=W, reiterating that there is no change in internal energy.