Isothermal Process
PV = const — see hyperbola on PV plot.
Key Notes
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).
Formulas
Equation of state
Boyle's law at constant T.
Work done by gas (expansion)
Logarithmic — moderate work compared to other processes.
Heat absorbed
Equal to work since ΔU = 0.
Internal energy change
Isothermal + ideal gas ⇒ T unchanged ⇒ U unchanged.
Important Points
Isothermal ⇒ ΔT = 0, ΔU = 0 (ideal gas).
All heat absorbed becomes work output (or work in becomes heat out for compression).
PV = const ⇒ hyperbolic curve on PV diagram.
Slow expansion in contact with thermostat — heat flows in continuously to maintain T.
Isothermal work is LESS than adiabatic work for same V change (slope shallower).
Real isothermal processes are SLOW — fast processes are usually adiabatic.
Isothermal Process notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.