Isothermal process – what remains unchanged? In classical thermodynamics, an isothermal process is defined as a process that proceeds at constant temperature throughout. Which statement is always correct about an isothermal process (for any substance, not necessarily an ideal gas)?

Introduction / Context:
An isothermal process is one of the classic thermodynamic paths, frequently contrasted with isobaric, isochoric, and adiabatic processes. Many students confuse what exactly must remain constant for isothermal behavior and what may depend on the working substance's equation of state (ideal gas versus real substance). This question clarifies the always-true feature of an isothermal process.

Given Data / Assumptions:

• The term “isothermal” literally means constant temperature.
• No assumption is made that the working fluid is an ideal gas unless explicitly stated.
• Other properties like internal energy and enthalpy may or may not vary depending on the substance and path.

Concept / Approach:

By definition, an isothermal process maintains a constant temperature T from initial to final state. For an ideal gas, internal energy u and enthalpy h depend only on temperature; therefore, in that special case du = 0 and dh = 0 for isothermal changes. However, for real substances (e.g., liquids, vapors near saturation, non-ideal gases), u and h can change even if T is held fixed, because intermolecular effects may alter these properties with pressure or specific volume at constant temperature. Thus, the universally correct statement is the constancy of temperature, not necessarily of u or h.

Step-by-Step Solution:

Verification / Alternative check:

For water at fixed temperature near saturation, changing pressure at the same temperature (e.g., through phase proximity) can alter enthalpy and internal energy significantly, proving that Δh and Δu need not vanish in general isothermal processes.

Why Other Options Are Wrong:

No change in enthalpy / internal energy: True for ideal gases but not universally valid.All of these: Overgeneralizes ideal-gas behavior to all substances.None of these: Incorrect because temperature is indeed constant by definition.

Common Pitfalls:

Blindly applying ideal-gas results to real fluids; ignoring property dependence on variables other than temperature. Always check the substance model before asserting constancy of u or h.

Final Answer:

there is no change in temperature