isothermal process
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An isothermal process is a change carried out at constant temperature — the system is held at one steady warmth from start to finish. Imagine a gas in a cylinder sitting in a large, well-stirred water bath: as the gas slowly expands, the bath keeps topping up the energy it loses, so its temperature never wavers. The word literally means "same temperature."
Keeping temperature fixed usually demands a constant traffic of heat. As an ideal gas expands isothermally, it does work pushing outward, which would normally cool it — but heat flows in from the surroundings at exactly the rate needed to hold the temperature level. For an ideal gas, whose internal energy depends only on temperature, holding T constant means ΔU = 0, so the first law gives a clean result: the heat absorbed exactly equals the work done.
Isothermal changes are the slow, patient, near-reversible kind: gentle enough that the system stays in step with a temperature reservoir the whole time. They form two of the four legs of the idealized Carnot cycle and anchor much of how we reason about the maximum work a process can deliver.
Let a gas expand very slowly inside a cylinder kept in a 25 °C water bath. The bath feeds heat in just fast enough that the gas stays at 25 °C the whole way — an isothermal expansion.
Temperature held fixed by a reservoir; heat flows in to match the work done.
Isothermal is the mirror image of adiabatic. Adiabatic blocks all heat and lets temperature move freely; isothermal holds temperature fixed by letting heat move freely. A truly isothermal change must also be slow — fast changes leave the system no time to swap enough heat with the surroundings to stay at one temperature.