Isothermal Process

Isothermal process: temperature stays CONSTANT throughout (ΔT = 0).

For an ideal gas: ΔU = 0 (U depends only on T).

First law: Q = W. All heat in becomes work out (or vice versa).

On a PV diagram: HYPERBOLA (PV = constant, Boyle's law).

Work done by gas: W = nRT·ln(V_f/V_i) = nRT·ln(P_i/P_f).

Slow expansion in contact with thermal reservoir at constant T ⇒ approximately isothermal.

Slope on PV diagram: less steep than adiabatic (because P drops less for same V increase).

Used in: refrigeration cycles, theoretical engine analysis (Carnot cycle).