Isothermal Processes

An isothermal process is a thermodynamic process occurring at constant temperature. Heat slowly flows into or out of the system to maintain thermal equilibrium. Examples include boiling water into steam at 100°C or freezing water into ice at 0°C. An ideal gas can also undergo isothermal expansion or compression while maintaining constant temperature.

Internal energy depends only on temperature. Since temperature remains constant during an isothermal process, the change in internal energy is zero. According to the first law of thermodynamics, when internal energy change is zero, the heat added to the system equals the work done by the system.

During isothermal compression, the gas volume decreases while pressure increases. The relationship between pressure and volume follows a hyperbolic curve, since pressure is inversely proportional to volume for an ideal gas at constant temperature. The pV product remains constant throughout the process.

Work done by an ideal gas during isothermal expansion is calculated using the formula W = nRT ln(Vf/Vi), where n is moles, R is the gas constant, T is temperature, and Vi and Vf are initial and final volumes. For example, expanding 1 mole of gas at 300 K from volume V to 2V yields approximately 1728.85 J of work.

In an isothermal process, heat added to the system equals work done by the system. Since internal energy change is zero, all heat energy transferred into the system is converted to work. This direct equivalence simplifies calculations for isothermal expansion and compression of ideal gases.

When a gas in a sealed syringe is slowly compressed at constant temperature, its volume decreases and pressure increases. Heat flows out of the system to maintain thermal equilibrium. The temperature remains constant despite the compression, distinguishing isothermal processes from other thermodynamic processes.

The pV curve for an isothermal process is hyperbolic, reflecting the inverse relationship between pressure and volume. This curve shape indicates that as volume decreases, pressure increases proportionally to maintain constant temperature. The hyperbolic path distinguishes isothermal processes from other thermodynamic paths on a pV diagram.